This popularised version of the political compass has now been around for over 20 years, and by that metric, this post is a bit late to the party, however the concept of expressing political alignment using 2 dimensions is far older than this.

The American libertarian David Nolan came up with his “Nolan Chart” way back in 1969. It is very US-centric, and was created specifically with the goal of converting people to libertarianism, however I can't help but feel that despite this, it is just more elegant than the political compass.

The more popular incarnation, that is the subject of so many political memes, has plenty of its own limitations and biases, but it also completely fails to be memorable (“Authoritarian-Left” doesn’t exactly roll off the tongue). Thankfully John Nerst at EverythingStudies wrote a pair of posts back in 2019 that reformulate the whole idea, addressing many of the limitations, and it is his “tilted political compass” that I want to build on.  If you haven’t read those two posts, and are interested in the subject of political alignment, I strongly recommend that you do so right now.  This post will still be here when you get back!

As a very brief summary, he proposes changing the axes from “Left-Right” and “Authoritarian-Libertarian” to “Thrive-Survive” and “Coupled-Decoupled”, in such a way that these new axes cut diagonally across the old ones, as follows:

In decoupled society the default relationship between two people is that of no obligations whatsoever… The only obligations are to respect explicitly stated rights and agreements. No expectations beyond that are valid.

In coupled society what it means to be a good person or what may be required of you at any point is open-ended. There are not clear boundaries between people and you are expected to take others’ or society’s interests into account as much as your own.

In a “survive” scenario (think famine, war or zombie apocalypse) mistakes are costly, outsiders are potential threats, keeping order is paramount and we can’t afford to be too generous towards the weak lest they pull us down with them.

In a “thrive” scenario by contrast (think true post-scarcity in a future automated economy), where we don’t even need to think about making a collective living we can afford almost limitless generosity towards the “other”.

When I first read these two posts, I loved them immediately.  The change to using an axis of “Thrive-Survive”, inspired by a SlateStarCodex post, readily conjures up worldviews and behaviours that align quite well with the politics it aims to describe.  The second axis of “Coupled-Decoupled” is a very useful concept that rather neatly expands the spectrum into a plane that maps very well onto the original political compass, whilst providing more insight and being more descriptive.

Looking at Nerst’s compass alongside Nolan's chart, you could be forgiven for thinking that he has reinvented the wheel, but I would argue that Nerst's compass is much deeper, more general, and less US-centric. At first glance, “Thrive-Survive” feels a bit like “Economic Freedom”, and “Coupled-Decoupled” feels a bit like “Personal Freedom”. However, whilst the “Freedom” axes seem to work pretty well (people on the right generally like lower taxes, which counts as economic freedom, and people on the left generally like bodily autonomy which counts as personal freedom), they aren’t able to explain some correlations between political views quite as effectively.

For example, if the right is defined by being pro- economic freedom, you might expect right-wing people to be in favour of immigration, as this allows people access to cheaper labour. Generally speaking though, the right is often more concerned with reducing immigration than the left. This is very easily explained however by the right being defined by a Survive perspective instead. 

Similarly, if the left is defined by being pro- personal freedom, you might expect left-wing people to be very in favour of free speech. Again however, the left is often more willing to compromise on free speech to achieve other aims.  The Nolan Chart’s “left” is labelled “Liberal”, which shows its US-centricity - Socialism was such an anathema in 1970s America, that there was no need to fit it into the chart! Personal freedom is much less of a core value for Socialists than it is for Liberals.  As such, if we want to include the whole gamut of left wing ideology within the compass, we have to use a different measure for our axis.

John Nerst also demonstrates that this formulation does an excellent job of explaining why the left-right axis in Europe behaves so differently to the left-right axis in the US. This framing of political alignment gave me plenty to think about, and I've wanted to write down these thoughts for some time.

"The Ideal Human (according to each quadrant)"

I was intrigued to find that Nate Silver recently wrote an article in which he basically rediscovered something like this “tilted political compass” framing of politics, just missing the top quadrant.  This suggests that despite being several years old at this point, the ideas in the EverythingStudies posts are still both useful and heterodox.  I hope therefore, that post is just as relevant to the present political situation as when Nolan first conceived his chart 55 years ago.

The Axes

The Thrive-Survive axis is perfect - as mentioned above, it needs very little explanation.  Sadly, the Coupled-Decoupled axis is rather more subtle - they are not the most descriptive words, requiring explanation before their meaning becomes clear.  What is more, Coupled and Decoupled were originally used in a cognitive sense, rather than a political one, meaning that further disambiguation is required.

As such, I would be strongly inclined to use some other words that more readily conjure up the concepts that are being described.  The words that I have come up with for either end of this axis, that I think are the most immediately expressive of the concepts being alluded to, are to describe individuals within a society as being either Atomised from each other, or Obliged to each other.  Replacing Coupled-Decoupled with Obliged-Atomised makes no fundamental change to the model, but reduces the need to preface the model with an explanation about what is being meant by societal coupling.  Going forwards I shall use this language.

Bottom Quadrant

Like John Nerst himself, “Atomised-Thrive” is the quadrant that feels like home to me. Classical Liberalism describes this quadrant very well, and J.S. Mill’s “On Liberty” provides an excellent reference point.  Of course, in the US, the label Liberal has rather unhelpfully taken on a more left wing connotation, but the EverythingStudies posts have already dealt with this at length.

It has been suggested that Libertarianism is the extreme of Liberalism, but I disagree with this assessment - Libertarianism is neither sufficiently extreme nor sufficiently Liberal to qualify.  Whilst strongly prioritising personal freedoms and a very Atomised society, current Libertarian movements are not very focused on “Thrive” concepts such as encouraging human flourishing, preferring instead to prioritise property rights as a panacea.  Equally though, they do not appear to be focused on “Survive” either, as a fairly critical presumption of Libertarianism is that; even with a very bare-bones government, everything will basically be fine.  This puts Libertarianism towards the edge, in between the bottom and right quadrants.

For the extreme of the bottom quadrant, the only label that makes sense to me is Anarchism.  This extreme represents an absolute atomisation of society, resulting in a complete absence of formal structures, combined with a confidence that we live in sufficiently bounteous times that humanity will not immediately start tearing itself apart.  Although Anarchism is perhaps perceived as less worrying than a column of marching Fascists, due to its inherent disorder; it would still be dangerous to view this kind of extremism as entirely benign.  I personally am not convinced that we are living in a sufficiently bounteous era, and therefore I would argue that by its very nature, Anarchism implies the death of civilisation itself.

Top Quadrant

The label of Populism for the top quadrant doesn’t quite work for me, because the particular thing that happens to rile people up at any given time can vary significantly (EverythingStudies does mention that this isn’t an ideal label).  A populist is a politician that shamelessly adopts whatever policies are being pushed by those that are shouting the loudest at the time; regardless of whether they think that they are wise, simply to improve their chances of being elected. I don’t think that Singapore is particularly populist, but I would consider it to be a very good modern example of an Obliged-Survive society.  The heavy-handedness of the Singaporean government (for example, outlawing chewing gum, heavily restricting immigration or requiring an exceedingly expensive permit to own a car) ultimately enforce a kind of cultural unity, and facilitate an orderly and efficient society.

I prefer to label this quadrant Nationalism, as this feels very descriptive of the Obliged-Survive approach to society. A Nationalist country behaves a bit like a family unit - everyone has obligations to it (and therefore to each other), and in exchange the country has a duty to protect all of its citizens and its culture from threats domestic and external.  As EverythingStudies notes, the mid-20th Century issues with Fascism, which is the extreme of this quadrant, made this whole quadrant feel toxic.  The label of Nationalism is similarly contaminated by this association, and is sometimes used as a pejorative:

This comic is a good example of this conflation. I don’t like the idea of using patriotism to describe the top quadrant, as this would suggest that people in the other quadrants can’t be patriotic.

Whilst Nationalism doesn’t align with my personal politics, I think it is very harmful for it to be considered universally bad, as such judgments tend to drive people more towards the extremes.  There is nothing uniquely bad about the combination of “Obliged-Survive”, it is just another perspective on the world that has some benefits and some drawbacks.  The furthest reaches of this quadrant may be most accurately called Fascism, but name calling only serves to shut down discussion.  After all, every quadrant has its extreme point, and if we were to conflate the extremes with the entire quadrant, that would be the death of any attempt at civilised conversation.

Singapore is a perfectly reasonable society, and whilst I would personally prefer to live in a more free and liberal country, plenty of people like it, and it is very successful.  Treating Nationalism as just another viable option, leaves more room for people to come together and compromise.  

Left & Right Quadrants

The left and right quadrants could really do with some more descriptive names.  Socialism works for the left, “Obliged-Thrive” quadrant - it is a generic enough ideology, with many possible qualifiers - democratic socialism, liberal socialism, nordic socialism, etc. These are all variants that cover different implementations of an overarching philosophy.  At its extreme, Communism is a fairly descriptive label, which much like Fascism, evokes shudders from a good proportion of the public.

How then can we describe the right?  Conservatism doesn’t really work, as this is not really precise enough - conservatism can mean traditionalism, which is very much aligned with the survive end of the Thrive-Survive axis, but is not specifically “atomised” (traditionalist central planners exist, and definitely don't fit in this quadrant).  Conservatism can also be used to describe a position of favouring the status-quo, or making small incremental changes as opposed to radical shifts.  It is only through the branding of certain political parties that it has come to be synonymous with the right in certain geographies.  Capitalism doesn’t really work either - despite free markets and capitalism being quite aligned with the “atomised” end of the Obliged-Atomised axis, it doesn't really have an affiliation to either survive or thrive.  Traditionalist capitalists absolutely are in the right hand quadrant, but progressive capitalists are in the bottom one.

The term “Neo-Liberal” could be used to describe this quadrant, but I personally hate this term: it is confusing (we have already used the term “Liberal” once), and it is not at all descriptive, requiring a history lesson to properly understand what “Neo” represents, and why it is fundamentally different to classical Liberalism.  I am instead inclined to use the word Corporatism to describe this quadrant.  Below is a quote lifted from the Wikipedia article:

Corporatism is a political system of interest representation and policymaking whereby corporate groups, such as agricultural, labour, military, business, scientific, or guild associations, come together on and negotiate contracts or policy on the basis of their common interests. The term is derived from the Latin corpus, or "body".

Corporatism does not refer to a political system dominated by large business interests, even though the latter are commonly referred to as "corporations" in modern American vernacular and legal parlance; instead, the correct term for this theoretical system would be corporatocracy.

Importantly, this is quite a broad term, which fits well with having to describe a whole quadrant.  Similar to the other quadrant labels, there are a variety of different ways to implement Corporatism, some of which have overlap with the other quadrants.  The general principle encapsulates a kind of contract based, dog-eat-dog worldview that seems likely to arise from an “Atomised-Survive” society.  Corporatism also treats these non-governmental entities as the primary agents and stakeholders in any kind of action or negotiation, which appears to align well with political parties in this quadrant, who prefer such things as privatisation and industry self-regulation over state control.

The extreme of this quadrant is an interesting one, as I don’t believe that it currently has a consistent or recognisable name.  “Far-right” is most often used to describe Fascism, which sits in the top extremity, rather than the right-hand one.  “Anarcho-Capitalist” is also a possibility, and is often used to describe extreme Libertarianism, but like Libertarianism itself, this doesn’t really fully encapsulate the Survive perspective. It is also too similar a word to Anarchism, which we have already used for the bottom extremity.  

Corporatocracy is explicitly mentioned in the above quotation, as meaning something different to Corporatism, but helpfully a Corporatocracy is a kind of government you are likely to get when Corporatism is taken to extremes.  Specifically, it is what Corporatism becomes when the corporations become too powerful and start to either dominate or replace the government.  Given the already existing confusion about these two similar sounding concepts however, this is not the best label either.

Where would we end up though, if we took the already extreme situation of Corporatocracy, and pushed it even further? Companies are already much like governments, insofar as they have enormous power over their employees for 8 hours a day, 5 days a week, and whilst they might pay taxes to a higher power, the more autonomy they have within the system, the more they appear like a state in their own right. In this Corporatocratic dystopia, we would end up with a large number of almost serf-like employees, working for a small number of very wealthy executives, able to lord their power over the masses. I have effectively just described the feudal system, with vassal lords commanding serfs, and paying homage to a distant and comparatively weak ultimate ruler.  Thus, I am inclined to call the extreme of this quadrant Feudalism - it may conjure images of medieval peasants, but the fundamental structure is very similar.

Taking the four quadrants as described above, I asked Dall-E to give me D&D style characters that represent each position.  Here are the ones that I liked the best:

The Centre

The centre hides a lot of conflict - you could land in the centre by being indifferent to most questions, but equally, you could land there by feeling very strongly about many questions in such a way that they average out to a centrist position.  In this way, it is possible to have two centrists that disagree about almost everything.  For example, on the Thrive-Survive axis, someone could be simultaneously very strongly pro-police (Survive), whilst also being strongly pro-immigration (Thrive).  This would not be a completely unreasonable position to hold, but I think it may be quite unusual.

The axes of Thrive-Survive and Obliged-Atomised have been settled upon precisely because they seem to cut through the space of political opinions in a sufficiently coherent way that such combinations of views remain quite rare.  Nevertheless, it is only a model, and it is possible that some future seismic political event could result in a shift in views that renders it obsolete.

My take on the political compass therefore looks like this:

Extending the Model

No model is complete without an attempt to make it cover far more ground that was initially intended.  EverythingStudies has already come up with a number of variations on the axes and quadrants that map remarkably well onto the diagram, so instead of doing more of the same, I propose some other dimensions that are not yet captured by the existing two dimensional model.

The first of these dimensions comes from yet another EverythingStudies post, in which John Nerst describes himself as Liberal, Progressive and Conservative.  By this, he is meaning: Liberal as described by the bottom quadrant; Progressive in the sense that he seeks to improve things, as opposed to a Traditionalist who seeks to keep things the same; and Conservative in the sense that he seeks gradual or incremental change rather than radical change or revolution.

I think that an axis of Progressive vs. Traditionalist maps fairly well onto the Thrive-Survive axis.  Whilst any such mapping is not perfect, there is an implication within the idea of Thrive, that there is enough slack in the system that improvements can be achieved. Of course, the exact direction in which progress is being sought will depend heavily on other considerations, and they might not align with how people in the US colloquially use the term “progressive”.  Similarly, there is an implication within the idea of Survive, that things that have already been proven are safer, and that untested approaches risk leading us to disaster.  This is probably why both Liberals and Socialists are often associated with Progressivism, whilst Nationalists and Corporatists are often associated with Traditionalism. In the future it is possible that these concepts will diverge, and we will see a large number of Progressive Nationalists, or Traditionalist Socialists, rather than these being very fringe ideas, but until then it seems like a bit of a waste of an axis.

This leaves the idea of an axis of Gradual vs. Radical, which I would argue is not well captured at all by the existing two axes.  Of course, you could argue that I have just made the assertion that Traditionalists are resistant to change, while Progressives embrace it, therefore this is also covered by the Thrive-Survive axis, but I do not believe this is the case.  This axis refers to the speed of change, rather than its direction.

There exist Radical Traditionalists that want to see society immediately revert back to a previous state, and there exist Gradual Progressives (like John Nerst) that want to see any potential improvement be made steadily and incrementally, to allow society to mitigate any unforeseen consequences.

This Gradual-Radical axis is quite well aligned with another conceptual spectrum - the divide between ideology and empiricism. People that subscribe to an ideology, and see the world through a particular lens, are likely to want to immediately address any issues they perceive.  In contrast, those that are less ideological, and prefer to see empirical evidence before proceeding are much more likely to support an incremental approach.  Philip Tetlock’s Hedgehog and Fox refer to a similar idea - the ideological “hedgehog”, making bold claims and advocating bold solutions, and the empirical “fox”, equivocating between different conflicting theories, and demanding a proven result before committing to further movement.

Into the fourth dimension

The second of these additional dimensions is another idea that at least initially appears very similar to Thrive-Survive.  When we think of the Thrive-Survive axis, at least as it has been used by SlateStarCodex and EverythingStudies, it is largely an inwards looking concept.  Whether the society itself is abundant with plenty or struggling to cope, providing individuals with opportunities, or protecting them from threats.  What happens if instead of looking inwards at the society that our politics is governing, we instead look outwards at the wider world?

When we look outwards, we can either choose to keep ourselves to ourselves, studiously maintaining neutrality, or we can intervene, aligning ourselves with other societies and against others.  There is already an established naming convention for this - Doves vs. Hawks, though to keep it consistent with the other axes, I will go with the more descriptive but less poetic Neutral vs. Interventionist.
These labels do seem to suggest that this axis is predominantly military in nature, but Intervention doesn't have to be explicitly military.  Take China’s Belt and Road initiative - this is one of the most sweepingly interventionist pieces of foreign policy that has been pursued since the cold war ended.  At least on the face of it, the BRI is purely economic - a huge injection of over $1 trillion of debt into a selection of key infrastructure projects in Africa and Central Asia.  Of course, there is no free lunch here - the end result of this investment is considered by many to be debt-trap diplomacy which is just yet another technique that countries can use to gain influence over one another.  The BRI does have a military angle as well, but this is only one of several strategic objectives that China is pursuing, including increasing soft power, diversifying trade networks and opening new markets for export.

I think that this dimension is critically important to understanding how and why people’s voting patterns and political preferences can shift very rapidly under certain conditions.  When foreign policy is not high on people’s agendas, some people may be very well aligned with a particular political party, even if they don’t necessarily see eye-to-eye on some specific policies such as military funding or international relations.  When the global environment becomes sufficiently turbulent however, all of these other points of agreement can become secondary to the pursuit of their desired geopolitical outcome.  Suddenly people can become willing to hold their nose and vote for someone they broadly disagree with, just because they agree with a particular foreign policy approach. If we combine this Neutral-Interventionist axis with the Thrive-Survive axis, we can provide some very informative examples of each pairing.

Warning - extreme simplification of complex geopolitics incoming:

Neutral-Survive - Switzerland is committed to neutrality, but at the same time they have a very strong military and have laws mandating nuclear shelters in many buildings.

Neutral-Thrive - Costa Rica has entirely disbanded their military, preferring to invest more in education and health instead. Although they are closely aligned with the US in some senses, because they would rely on the US military in the event of an attack; they still strive to remain largely unaligned to avoid giving anyone a reason to attack them.

Interventionist-Thrive - NATO, whilst a defensive alliance, has many members that have historically been quite comfortable with “exporting democracy”, and most European countries along with the US Democratic Party are fairly Liberal, giving NATO a relatively “Thrive” perspective.

Interventionist-Survive - Iran and Russia are also highly interventionist (Iran through their funding of Houthi rebels, Hezbollah and Hamas, and Russia through their invasions of their neighbours), whilst being firmly Nationalist, and framing these interventions as necessary for their country’s survival.

Visualising the 4 axes

Feel free to skip this section if you just want me to get to the point.

The additional axes make it no longer possible to express one’s position on a simple 2x2 grid.  The first thing that came to my mind when thinking about four axes was the Myers-Briggs personality type model.  This approach to personality classification is often criticised, but DynoMight has mustered a very good defence of it here.  DynoMight’s adjustments to the basic MBTI model are very relevant to the discussion of political alignment too, so if we adopted this style of presentation, a similar approach of capital letters for strong views, lower case for weaker views, and x for centrism would be appropriate.

These four axes are then:

So someone mildly Interventionist, but strongly Radical and Socialist would be an “OTiR”, and someone strongly Libertarian, Gradual and Neutral would be an “AxNG”.  This would make me an “atig”, as someone that is Atomised, Thrive, Interventionist and Gradual, but not particularly extreme on any of these views.

Whilst this was my first thought, I don’t think it is likely to catch on.  People generally prefer descriptive labels, and whilst the Myers-Briggs Type Indicators have their die-hard fans, this alphabet salad is unlikely to capture the imagination of many people.

My second thought was about animals.  The two new axes already have animals associated with them - Fox and Hedgehog; Dove and Hawk.  There are some fairly obvious associations for the original two axes as well. Dogs and Cats are fairly stereotypical exemplars of animals behaving in an Obliged and an Atomised manner respectively.  Finally, the general attitude of “things will be fine” vs. “things will be terrible” that oversimplifies the Thrive and the Survive perspectives, are very much embodied by Wall Street’s Bulls and Bears cliché.

This probably isn’t very helpful either, but it does give us a great opportunity to get Dall-E to draw some anthropomorphised animals arguing about politics:

A Second Compass

I finally settled on a much simpler idea - a pair of political compasses (pun very much intended).  We already have the first, which offers significant insight into modern political differences, and the meaning of “Left” and “Right”.  What happens if we combine the two new axes into their own separate compass - what insight might that provide?

We can characterise the 4 different axes as follows:

Therefore the original political compass covers the axes expressing our views on “individuals’ duties to one another” and “the purpose of society for its people” - these could be summarised as “how you think the world should act on you”.  The two new axes express our views on “society’s role in the wider world” and our preferred “approach to making changes” - in contrast to the first compass, these could be summarised as “how you think you should act on the world”.  On this basis, I will now refer to these as the Inwards Compass and the Outwards Compass respectively.

This Outwards Compass gives us another four quadrants, and this time there is not an obvious way around to place the axes.  I have chosen Gradual-Radical from bottom-left to top-right, and Neutral-Interventionist from top-left to bottom-right, because that is how it seemed to naturally align itself in my head.  If you prefer it another way, don’t let me stop you.

The names I have picked for the four quadrants are hopefully reasonably descriptive:

I asked Dall-E for some more D&D characters that were representative of these labels, and these were my favourites:

Outwards Extremes

As with the original political compass, these are all potentially perfectly reasonable approaches, but any one of them could be problematic if taken to extremes.  The issues with extreme Interventionism and Radicalism are fairly obvious, but it is also harmful if Neutrality turns into isolationism, or if a preference for gradual change turns into a resistance to any change at all. 

Whilst many people are quite happy to be considered Interventionists or Radicals, I chose to name the other ends of these axes Neutral and Gradual, because the extremes of Isolationist and Stagnant are pretty negative.  It is important that the labels of the axes themselves resonate with people, as otherwise they do a poor job of expressing the range of opinion in the population.  If the axes are labelled in an unappealing way, everyone will simply consider themselves to be a centrist.

If we are specifically discussing labels for the extremes though, we don't have to worry about their mass appeal.  With that in mind, I offer the following labels:

Cenobite as the extreme of Gradual and Neutral - cenobitic communities were both isolationist and unchanging.  An example of this might be Japan’s Edo period, which is renowned for its commitment to isolationism, and its resistance to change.

Machiavellian as the extreme of Gradual and Interventionist - Machiavellian is used to describe plotting, duplicity and the pursuit of power above all else.  The British Empire should definitely be a contender for this, playing opponents off against each other over centuries, and manipulating entire continents for its own gain, without regard for the cost to anyone but itself.

Zealot as the extreme of Radical and Neutral - zealots are uncompromising in their pursuit of their ideals, but are often unconcerned about those outside their sphere of influence. During its Cultural Revolution, China was isolationist, but also engulfed in internal turmoil as its government sought to make radical societal changes whilst enforcing strict ideological purity.

Militant as the extreme of Radical and Interventionist - militants are also uncompromising, but their focus is often on bringing the world into line with their ideology.  Cuban Revolutionaries, supporting guerilla warfare across South America fit this category - offering their help to any that were willing to take up cause against the US and global capitalist interests.

This gives me an “outwards compass” that looks like this:

Alternative Compasses

Feel free to skip this section if you aren't interested in alternative formulations.

The axes don't necessarily have to be paired together in this way. Personally, I quite like this approach, as the inwards compass is very recognisable and clearly shows the left-right divide, whilst the labels for the outwards compass feel very natural and informative. Given my earlier mention of geopolitics however, I feel that briefly exploring alternatives is worthwhile.

We could instead pair "Thrive - Survive" with "Neutral - Interventionist" to form one compass, and "Obliged - Atomised" with "Gradual - Radical" to form the other. This first compass then covers society's purpose for its people and role in the wider world, and I have already described its quadrants above:

The second compass could then be considered to cover something like the "size" and "speed" of a society. A very obliged society is one in which decisions necessarily affect a large number of people, and is therefore in some sense "large". Similarly a radical society makes changes quickly and is therefore "fast". In Nassim Taleb's book Antifragile, he discusses at length the idea that things being large and fast makes them fragile, and that systems that allow for gradual change across many smaller entities may achieve what he terms "antifragility", where they are not just robust against shocks, but actually gain from disorder. This allows me to use (abuse?) this concept and terminology for this compass:

I am inclined to call these two compasses the "Geopolitical Compass" and the "Momentum Compass", and I think they do offer additional insight. Whilst I might not agree with the positions, I can at least understand the appeal of all of the quadrants on the inwards and outwards compasses, such as Nationalism or Idealism. This arrangement of axes however yields one quadrant that I just cannot fathom.

It is hard to see the label "Fragile" as anything but negative, so in line with my previous points I have changed it to "Coordinated", because a society would have to be very well coordinated to be able to withstand rapid changes whilst being so interconnected. Perhaps it is my bias showing, but I think fragile is a better fit. An obliged society has a myriad of dependencies both visible and invisible, by the very nature of people being obliged to each other, making it a complex system. Most attempts to make rapid changes to a complex system are going to be a disaster, because there will inevitably be interactions that haven't been considered.

The "Coordinated" quadrant is the one in which Socialist and Nationalist revolutionaries reside, and I have always had a problem with the "everything is terrible, let's burn civilisation to the ground so a new, better society can rise from the ashes" point of view. In contrast, Liberal or Corporatist revolutionaries aren't really a thing, simply by their atomised nature - the entities that someone in the "Agile" quadrant might try to revolutionise are generally smaller than literally the entirety of civilisation, so when things go wrong, it has less scope to be catastrophic.

The third possible pairing of axes is "Thrive - Survive" with "Gradual - Radical" for one compass, and "Neutral - Interventionist" with "Obliged - Atomised" for the other. To me, the addition of "Gradual - Radical" to the concepts of Thrive and Survive, makes each quadrant feel like a mood or vibe.

Survive, as ever, evokes the idea that "civilization is hanging by a thread", but combined with Gradual, suggests a kind of knife-edge, tightrope walk situation where things are precarious, so you mustn't make any sudden moves. In contrast, Radical suggests a kind of desperation - no small measures will save us, it's our last chance so go big or go home!

Thrive combined with Gradual seems fairly straightforward - a kind of cautious optimism, that I'd describe as hopeful. Things are pretty good, so let's keep improving them carefully. It is its combination with Radical that I found more tricky to describe. After all, the drive to do things quickly is unlikely to be due to desperation, as this goes against the fundamental basis of a Thrive mindset. Instead, the need for speed is more likely to be driven by the presence of a burden - either the realisation that you only have one lifetime to accomplish everything you have set out to do, or the guilt of living in comfort while others are not as lucky, driving a desire for rapid changes to address the disparity.

These labels are definitely less appealing than those of the previous compasses, but it is important to note that they are descriptions of how we view society, and not descriptions of people themselves.

This leaves the final pair of axes to analyse. I found myself visualising these almost like characters or personalities. The Obliged ones are motivated to act on behalf of others - either in an inwards looking way, to guard their society, or in an outwards looking way, to march out and save their society from external threats.

The Atomised ones in contrast, can probably take actions more freely, choosing how and when to get involved. The Neutral quadrant preferring to observe, avoiding entanglements, and the Interventionist quadrant being more inclined to get stuck in and "play the game".

On this basis, I shall call these two compasses the "Mood Compass" and the "Character Compass". My first impression is that this framing is less useful than the other two - at the very least, I didn't get any flashes of inspiration or understanding from it. I also like these labels the least - they sound a bit contrived, and I'm definitely overloading the words, trying to encapsulate a lot of nuanced meaning within the two-word phrases. Nevertheless, I have included it here both for completeness, and because it may be useful to other people who have a different perspective.

This gives us three ways to label each of the sixteen possible positions:

The "Inwards & Outwards" column definitely seems the most useful and relatable to me, so I am happy to leave further exploration of the alternatives as an exercise for anyone that finds them particularly informative or inspiring.

Conclusion

The combination of the inwards and outwards compasses covers all 4 dimensions that have been discussed, and hopefully provide a relatively concise and relatable description for a huge range of political views. I consider myself to be a Liberal Strategist, and am very comfortable with that label, but I also know people that I consider to be Socialist Crusaders, Liberal Idealists, and Corporatist Mediators, who I think would be very happy with those descriptions too. I will admit to not personally knowing any self-described Nationalists, though I think this is due to the fact that I am Liberal and that the inferential distance between Liberal and Nationalist makes it difficult to form such connections.  From what I can tell though, the label of Nationalist does appear to be slowly losing some of its stigma, so this may not be an entirely unwelcome description either.

Given that the previous attempts at breaking politics out from a single dimension have had very limited success, I don’t expect this to be anything more than a niche interest.  I do hope though, that it provides some people with either interesting insight, a useful mental model, or a jumping off point for research or introspection.  I would love to know what anyone that has read this post considers themselves to be, so if you got this far, please consider leaving a comment!

It has been some time since I posted on this blog.  Writing posts that are good enough for me to consider posting takes a reasonable amount of effort, and since my last post I embarked upon a new project that significantly reduced my time available to work on such things.  Given the title of this post, it will come as no surprise that the new project in question is “everything associated with having and raising a child”.  This project is probably of limited interest to some, but there are aspects of the experience that I feel that I should share, in case it is of benefit to others.

By “doing things differently”, I refer to the process of questioning why an approach to something may be the norm, and choosing an alternative path that is more optimal (for me at least - other people’s predilections may differ).  This of course carries risks, and I try to think through as many reasons why the norm is indeed the norm, before I cavalierly leap over Chesterton’s fence.  However, if after this process, I still feel that I can make my life easier/better/more efficient with minimal risk, then I give the alternative approach a try.

I had been planning to do a post at some point about general successes (and occasional failures) that I have had in doing things differently in life.  While I may yet do this, the specific situation of having a child yields more than enough material for its own dedicated post.  My inclination to write this post has grown gradually as I encounter more and more people that are on the fence about whether or not to have children.

The vast majority of media that I am witness to portrays parenthood as a thankless slog through sleepless nights and ego death which is justified by the platitude that “your love for them makes it all worthwhile”. On this basis, it is quite unsurprising that people are in two minds about the decision, and this has to be a contributing factor in the rapid global decline in fertility that Robin Hanson has recently been taking very seriously.

I can quite happily say that so far this is not my experience at all, however I have taken some unconventional approaches, which may have made a significant difference.  I went into this process with very low expectations - I was fully prepared for at least two years of hell, and the experience has been so much better than my wildest hopes that I can’t help but feel that we must be doing something right.  I really don’t identify with most of the sad tropes about stressed out miserable parents.  This drives me to want to share these approaches and my reasoning behind them, as they have been very successful for us, and may give other people ideas for how to make the experience work better for them.

Of course, some people may not be in a position where they can do some of these things - for example, I am based in the UK where taking parental leave is a legal right, whereas people in other jurisdictions may not be able to (the US - I’m looking at you).  I must also further caveat this with “your mileage may vary” - I am currently operating with a sample size of 1 and all babies are different.

Nevertheless, there are a large enough set of “weird” or unconventional things that we did, that some of them may be of some use, so if any of these approaches sound reasonable to you, feel free to take them.  This is a long article, so feel free to skip to any section that looks particularly interesting, but the ones that have been the most game-changing and foundational to our approach are 1 and 11.

1. Concurrent Parental Leave

2. Sleeping in Shifts

3. Combi Feeding

4. Baby Carrying

5. Taking a Long Holiday with the New Baby

6. Sign Language

7. Elimination Communication

8. Baby Led Weaning

9. Having a Flexible (and Late) Routine

10. Floor Bed

11. Both Parents Working Part-time

12. No Screen Time

13. Books and Letters

I am not trying to claim that we’ve invented anything new - I don’t doubt that we’re not the first people to have done any of the things described here, but even over 2 years in, I have yet to meet anyone that has done any of 1, 2, 5, 6, 7, 9, 10 or 11.  I am also not trying to claim that we have done absolutely everything perfectly.  While I am pleased to say that there are very few things that we would do significantly differently next time around, we were still learning as we went along.  Reading books can only get you so far, and at a certain point, we had to resort to trial and error to find what worked the best for our child as an individual.

Finally, I repeatedly say “we”, because I have been doing all of this together with my partner. She has not just been supportive and enthusiastic about some of my unusual ideas, but has come up with plenty of unusual ideas of her own.  Neither of us can take sole credit for any of the approaches below, as whilst either of us may have made the original proposal behind any particular idea, we have collaborated on all of them to make them work.  She has also read this essay and agrees with the sentiments expressed herein, so before anyone decides that “of course you have found it a positive experience, you’re a man - your partner is the one doing all the hard work”, I would like to address that trope head on.  We both try very hard to maintain an egalitarian relationship, and that is what initially drove us to take approaches 1 and 11, which have gone a long way towards helping us to avoid many of the common pitfalls of inequality in parenting (e.g. mother as default parent, learned helplessness and maternal gatekeeping, underappreciation of domestic/emotional labour, etc.).

With all that out of the way, let me get on with sharing our approach.

Concurrent Parental Leave

The first unusual thing that we did was to both take parental leave at the same time.  We each took 6 months off concurrently.  This was absolutely great, and I would recommend it to anyone that asked (as long as they were in a sufficiently comfortable financial position to utilise the full 52 weeks).  We will definitely be doing the same thing next time.

In the UK, you are entitled to 52 weeks of parental leave, which can be split however you like between the mother and father.  Uptake of this “shared parental leave” has been very low with only 2% of fathers making use of it, however in the cases where people have made use of it, most people take it sequentially, with the mother taking off the first 6 months and the father taking the last 6 months, or 9 and 3 months, etc.  A majority of the people that we have spoken to were not aware that the leave could be taken concurrently.

Although taking the leave concurrently means that you’ll both be returning to work when the baby is 6 months old, rather than a year old (I’ll deal with our approach to that later), it does have several advantages:

• Being there at the same time meant things were easier for both of us - an extra pair of hands makes many things take less than half the time, and be more than twice as easy.  You can go to the toilet on your own, you can make a sandwich, etc.  Seriously, it is hard to overstate how big of a deal this is.

• Not only is the essential stuff easier, but you’re able to do much more and be much less stressed and exhausted.  I’ll dig into two examples of this below, being travel and sleep.

• There is no worry for the mother regarding the father’s imminent return to work, leaving her alone to cope.  In the UK, fathers tend to get the first 2 weeks off, which allows them to help in the very early days, but many people understandably find it very difficult when this 2 weeks is over.

• This approach greatly facilitates equality by making it easy to ensure that mother and father are taking an equal role.  There is no period in which the mother is the sole caregiver, learning the ropes on her own, so the father can participate equally in all aspects of looking after the baby, and contribute to a shared understanding of what works and doesn’t work for the baby.

• It also means that both parents are taking an equal hit to their respective careers, so neither is sacrificing more than the other in terms of long term prospects.

• As both parents are equally present, the child isn't disproportionately clingy with one parent over the other.  They can usually go to either parent when there's a problem or they're upset.  They might still have occasional mum days and dad days (and to be fair, for us there were more mum days than dad days), but not exclusively one or the other.

• The baby doesn't get used to one parent always being around, which often makes an eventual change-over to the other parent at 6 months very difficult.

• The mother isn’t in the position of dealing with the difficult first few months, while the father takes over and gets the "victory lap" of 6-12 months, where the baby starts to crawl, might say first words and take first steps.

• It may possibly aid language acquisition, as there are always 2 people around talking to each other, rather than a single person with no-one to talk to unless they brave going out.

• In the UK, taking less than or equal to 26 weeks off means your employer is not legally permitted to make changes to your job.  This doesn’t necessarily mean that they won’t, but it gives you both recourse to challenge any changing of responsibilities that they might try to force upon you.

For ourselves, this was a wonderful bonding time for all of us.  It brought my partner and I even closer together as we supported each other on a very intense new learning experience.  We were able to work together as a team to overcome obstacles, share the burdens and the joys, and be far more adventurous than we would ever have been on our own.

Sleeping in Shifts

Sleep is a controversial topic, as everyone thinks they have “the solution” for getting babies to sleep, but inevitably all babies are different, so people’s advice may not actually be very helpful.  Thankfully though, I’m not actually going to talk much about the baby’s sleep - it’s the approach to our own sleep that was unusual and successful here.

Newborn babies don’t sleep through the night and need feeding every couple of hours, which means that anyone looking after a baby on their own will necessarily be sleep deprived for weeks on end.  Because we were both around for the first 6 months, we were able to deal with this in shifts.  In this situation, if you’re bottle feeding, it is fairly straightforward to take it in turns to feed a baby.  We opted to breastfeed, which made things a little more complicated, but ultimately we used a bottle for one feed overnight (more on this below).

By using a bottle overnight from 2 weeks old, I was able to take the baby for a 4 hour stretch, allowing my partner at least 4 hours of uninterrupted sleep (between a last feed around midnight, and a first feed around 4am, with a bottle feed from me halfway in between).  As the baby started sleeping longer, this was able to be stretched out such that before 1 month old, my partner was able to sleep a solid 8 hours a night (between a last feed at around 10pm and a first feed at around 6am, with me giving a bottle at 2am).

This shift-based pattern, with my partner going to bed some time between 10pm and midnight, and me going to bed between 2am and 4am worked incredibly well, and meant that both of us could operate with minimal sleep deprivation well before the end of the first month.  This is a dramatic contrast to several people that we have talked to, where the mother had not had an unbroken 8 hours of sleep for 2 months straight.  The avoidance of sleep deprivation ultimately meant that this period was much less stressful than it could have been, and it was much easier for us to support each other.

In fact, this pattern was relatively easy to flex as the baby grew older.  As they started sleeping in longer chunks, they would wake later in the morning and we could move the bottle feed gradually earlier.  By 2.5 months old, we had moved the bottle feed to before midnight, and the baby would regularly sleep through until after 8am. Your mileage may vary greatly here, and I think that we were exceedingly lucky to have a baby that slept so well, but our approach meant that if they hadn't been such a good sleeper, we would have been able to get enough sleep regardless.

The shift pattern also meant that I could stay with the baby while my partner slept, so that the baby wasn’t alone if and when it woke up.  This is something that we had read was recommended in Philippa Perry’s “The Book You Wish Your Parents Had Read”.  I therefore wasn’t desperate for the baby to go to sleep, so that I could go to bed too; as I wasn’t particularly tired, with my sleep cycle shifted by about 5 hours.  This made for a relaxed night-time routine, which was very helpful, as being stressed about bedtime is a surefire way to ensure that the baby won’t sleep.

Combi feeding

In general, from what I can tell, most people tend to go down the “exclusively breast-fed” or the “exclusively bottle-fed with formula” route.  I’m sure there are some people that do both, but a lot of the advice we read seemed to warn of things like “nipple confusion” or suggest that you only try introducing a bottle after 3 months.  This no doubt puts some people off, such that they don’t try it.

We couldn’t find any good evidence that “nipple confusion” was a real thing - only occasional anecdotes, and scare stories from dogmatic “breast is best” advocates.  The 3 months suggestion seemed to stem from the concept that feeding becomes a conscious action somewhere around that time, which can lead to things like bottle refusal around this time.  This was a useful thing to be warned of, but didn’t seem like a good reason not to try it.

The main concern that we could see around doing both, was that using formula milk for some feeds means that you are not stimulating your breast milk supply.  Depending on how many feeds were breast vs. formula, it is conceivable that this could cause issues.  With that in mind, we opted to use pumped milk for bottle feeds, which meant that the baby was technically still exclusively breastfed (but hey - to each their own - I am passing no judgement on people that use formula).

I started giving the baby 1 bottle of pumped milk each night when they were 2 weeks old, which as mentioned above, guaranteed my partner at least 4 hours of uninterrupted sleep.  As the baby slept longer and this became less necessary, we shifted to a double evening feed to tank the baby up overnight and enable them to sleep even longer before waking hungry.

We found that milk supply was higher in the morning, so pumping in the morning and using this at night was very helpful.  It was possibly also beneficial for sleeping, due to "overnight" hormones in morning milk.

We had heard that it is worth having a variety of bottles and teats, as babies can be choosy about them and refuse certain bottle styles.  We did indeed find that our baby was very picky, to the point where the only thing that they would reliably drink from was a Munchkin cup as pictured.  This meant they were actually drinking from a "cup" from 10 weeks old.  You go with whatever works!

Baby Carrying

This one is definitely not going to work for everyone, but we decided to exclusively use a baby carrier/papoose rather than a pram/pushchair.  In fact, we still don’t own a pram!  Our initial reasoning was fairly straightforward - firstly, we live in a large city with lots of steps near our house and even more steps to access public transport, making the idea of continually hefting one up and down all these steps unappealing.  Secondly, we didn’t really have much space in our house to store another huge item of what is effectively furniture.  Thirdly, prams all seem to be ridiculously expensive - we thought we would try it without one, to see if we really needed it.

There are certainly a few disadvantages to not using a pram - it is more physical effort to use a baby carrier, and you have less storage with you, so we often had to take a rucksack with us.  That being said, the initial reasoning that we used turned out to be pretty sound - baby carriers are much smaller and easier to store, and it was pretty easy going out and about without having to manoeuvre a pram through a bustling city.  Squeezing into cafés and shops was not a problem either, and it was great not having to worry about where to park a pram every time we attended a playgroup.  We also both got stronger as the baby grew, so the physical effort wasn’t actually that bad.

What we did find though, was that there was another huge advantage that we hadn’t even considered initially.  As the baby is much closer to adult eye-level, they get much more interaction and eye contact with other people as you walk around.  This naturally made it much more likely that people would talk to them, helping with sociability and possibly improving language acquisition.  It is hard for me to overstate how stark the difference was in this sense between being carried and being in a pram.  In a pram, down at hip-level, a child doesn’t spend a lot of time looking up at the faces of people around, and only the most exuberant of people will stop to wave at a child in a pram.  In a carrier on the other hand, we found that our baby was constantly looking at or smiling at (and sometimes shouting at) people passing by, and a majority of these people would at the very least smile back.

From about 6 months old, we started doing shoulder rides too, which was less tiring (the weight pushes directly down onto shoulders rather than pulling you forwards or back).  Shoulder rides are a bit more limiting, as you don’t have both hands free, but on the other hand, it is much quicker to pick up and put down the baby without a carrier.  Our child, being a bit of a daredevil, really loved this, and still quite likes this mode of transportation age 2.

The closest thing to a pram that we have now, is a sit-on scooter that we can push along, but this is so much tinier and more lightweight than even the most minimal pushchair.  It also requires more effort from the child - rather than simply sitting and relaxing, they have to engage their core and stay on, as well as giving them the opportunity to learn to steer.  This additional effort means that our energy levels aren’t completely mismatched - after a long day of walking around, we don’t have a hyped up toddler that has been sitting around all day, so we all get to have a bit of a relaxing evening.

Taking a Long Holiday with the New Baby

This is the one that comes up the most in conversation, and that people have consistently thought that we were absolutely insane for doing.  We flew to Mexico for 6 weeks with our 4 month old baby, and did a road trip from Cancún to Mexico City and back.  Personally, I can’t recommend it enough - after all, without taking a sabbatical, when else are you going to have the opportunity to go on an extended holiday like that.  Obviously, this only works if you’re both taking parental leave concurrently, but it is another great reason to do so.

We did build up to it of course - when the baby was born we visited family and worked our way up to longer car trips.  We then tried flying by taking a weekend trip to Bucharest.  Once we were comfortable with all of that though, it seemed pretty manageable.  The trip was a really great time, allowing the three of us to bond.  It also wasn’t particularly disruptive to our way of living, as at that point there was no existing rhythm to break out of - everything was still new to us anyway.

Travelling around a new country, we found that all of the walking involved helped us to stay fit without really thinking about it, though this may just be our approach to holidaying - I’m sure it would be possible to do less walking than we did!  People were also generally very kind and pleased to help with and interact with the baby. 

Fundamentally, we enjoy travelling, and didn’t want to stop just because we were now parents.  That being said, we did change our approach to make it enjoyable for the baby too - we avoided driving for too long on any one day, and we made sure to facilitate naps and snacks as required.  By now, we have travelled quite a bit with our baby, and despite a few people suggesting that they wouldn’t get much out of the experience, the reality appears to be quite the opposite.  We have generally found that significant developmental spurts seem to coincide with holidays that we take as a family.

Sign Language

Hand signs are much easier than words for a baby to coordinate and formulate.  This shouldn’t be too surprising, as even adults often find mimicking a new sound to be quite challenging, but mimicking a hand movement is much more straightforward.

Babies can understand things that are said to them far earlier than they learn to speak, so by coupling certain words with hand signs, the baby is able to associate the concept with the sign as well as the vocalisation.  This allows them to attempt to communicate much earlier, and when they can communicate even a rudimentary thought, this is very empowering.

We’re not proficient signers, so we weren’t anywhere close to saying everything both verbally and in sign language - we just used a few key signs that allowed for the most common concepts to be signposted.  These signs were: More, All Done, Food, Water, Milk, Potty, Yes, No, Mum, Dad, and Nappy Change.

For us, their first sign “potty” happened just before 5 months old, “more” at 6 months, “milk” around 8 months, with “food” and “water” at 11 months.

In contrast, their first word was at just over 8 months (“dad”).  Learning and using these few signs didn’t actually take a lot of effort, so I would say that it was worth it.  Only just though - largely because they took to speaking so quickly: first word at 8 months, 10 words by 12 months, 100 words by 18 months.  If they had taken longer to become verbal, the sign language would have been useful for longer.

On the other hand, I can’t rule out the idea that sign language could have itself aided wider language acquisition.  It would be very interesting to see a study on whether using basic signs with babies accelerates their use of verbal language.

As a side note, the other things that we did that we have reason to believe had a positive impact on language acquisition are:

• No dummy/pacifier - this seems to be a standard recommendation by doctors, so we decided to just never get one.

• No baby talk - we talk to them normally, without using cutesy child-specific words (like “horsey” and “din-dins”), which made recognition of words used in conversations between adults more easy.

• As mentioned above, both parents off at the same time meant conversations constantly happened around them.

• Similarly, baby carrying meant they were at adult eye level, so conversations when out and about didn't go (literally) over their head.

• The holidays were a break from normal routine, so different conversations and words were used.

• We've made great use of the Usborne “first thousand words” book, which quickly became a favourite, especially the “opposites” page.

As you can see from the above graph, word acquisition tracked pretty close to exponential.  While we stopped tracking individual words at about 18 months, because they were coming too rapidly to keep track, this trend has continued.

It took about 6 months to go from 10 words to 100 words, and after another 6 months, by age 2 they knew all the words in the “first thousand words” book, so definitely had well over 1000.  At 2 years and 3 months they had picked up words like “consequences”, “frustrated” and “antibiotics”, and my favourite sentence so far is “want to go on rocket to moon on adventure holiday”.

I say all of this not to brag (well ok, maybe a little - I am very proud of them), but to make the point that some of what we've done must have had an effect.  I'm not one for false modesty, so I’m comfortable saying that my partner and I are reasonably intelligent, but neither of us is John Von Neumann or Giuseppe Mezzofanti.  We therefore have no reason to expect that our child has superhuman language abilities.  The generally expected rate of language acquisition seems to be first word between 10 and 14 months, 100 words by age 2 and 1000 words by 3.  It seems likely to me that some of the approaches that we have taken will have contributed to roughly halving this doubling time.

Elimination Communication

This is an approach to nappies and potty training that focuses on giving babies an awareness of their bodily functions and the ability to communicate about them as early as possible.  Usually focused around noticing trends and cues from your baby, to allow you to put them on a (tiny) potty before they go in their nappy, and avoid them getting used to soiling themselves.  Many proponents of the various techniques claim that their babies have been “potty trained” at stupendously early ages.  This is probably best taken with a pinch of salt, but I can share our experience.

The concept of Elimination Communication is nothing new (hence there being an established name for it), however it definitely seems to be less prevalent in the UK than it is in the US, as most of the resources we came across were from the States.  Without wanting to stereotype anyone, it also seems that a large number of people currently practising and espousing this approach are quite far towards the “crunchy” end of the spectrum (by which I mean the lifestyle that is often typified by a kind of hippie organic vegan asceticism).  This is a little unfortunate really, as I don’t think there is any need for it to be associated with this, and the perceived association might put off people that have more conventional lifestyles.

We came across the general idea independently some time ago.  My partner spent some time living in China around a decade ago, while western brands and products were still trying to make inroads into their markets.  During this time, she encountered many families with quite young babies that did not use nappies at all, and seemed to be able to sense when their babies were about to go.  When out and about, these parents held their babies over bins, drains or bags to do their business, and seemed to have a remarkable amount of success.

It is my understanding that unfortunately these days most people in China look down on these practices, and tend to use disposable nappies as much as people in Europe and the US.  At the same time, in the UK at least, the average age of potty training completion has gone up from 2 ½ to 3 ½ in just the last 20 years, and 24% of children start school without being potty trained. The average baby also gets through around 10,000 disposable nappies, which are all either burned or get sent to landfill. After some research, and discovering that the idea of “Elimination Communication” seemed to be attempting to explain and codify a similar approach among parents in the US, we decided to give it a go.  Obviously, we’re not out there letting our baby defecate into bins, but we did invest in a number of tiny travel potties, and are intimately acquainted with the locations of public toilets in a large number of destinations…

The approach requires far more detail than I can include in this post, but we found that the most useful resource was “The Diaper Free Baby” by Christine Gross-Loh.  We didn't worry too much about some of the suggested actions such as overnight pottying or "naked observations".  We mostly just offered our baby the opportunity to use a potty at nappy changes and transitions between activities (sleeping and waking, feeding and playing, etc.).  Prompting the baby with cues when on the potty was also helpful for us (using a hand sign and grunting).

The other thing that we did, which seemed to help, was to use reusable nappies.  They are less absorbent, so the baby lets you know that it is dirty earlier.  This may sound unpleasant for the baby (after all, most nappy marketing focuses on how comfortable they will feel, despite having thoroughly wet/soiled themselves), but it avoids them getting too comfortable with soiling themselves, which is then something you have to train them out of doing later.  It results in you needing to change the nappy more often, so that the baby doesn’t get uncomfortable, but we were happy with that trade-off.  Mind you, we still used disposable nappies on holiday - they’re much more convenient, you can buy them at your destination, and you don’t need to wash or carry around a bunch of dirty nappies.  All in all, I think what we did roughly amounts to what some refer to as “Lazy EC”, but we found it to be immensely beneficial.

“Babies used to be potty-trained much earlier, and more willingly, because towelling nappies were so damp and uncomfortable. But the moisture-wicking technology of the disposable has made it possible for toddlers to sit for hours quite happily in their own feculence.”

The Telegraph, as ever, raging about the issue in much more hyperbolic terms

By providing the baby with a hand movement and a noise that was associated with going to the potty, the baby was empowered to be able to communicate their needs.  Our baby was able to signal to us by grunting that they were about to defecate by 4 months old.  This meant that we were usually able to get them onto the potty in time, which was actually a source of considerable happiness for our baby.  When you are that small and powerless, it must be reassuring to be able to control even a tiny amount of your world.  Despite requiring an initial investment of time and effort, it paid dividends much quicker than we had hoped, such that by 6 months old, we were hardly dealing with any dirty nappies - only wet ones, which was great when the baby had started weaning.  By this point, we also tended to read books on the potty to make the potty experience more enjoyable.

We started potty training at 19 months old, going cold-turkey using the “oh crap method”, and were able to do away with nappies entirely at 20 months old, even during naptime.

We still used reusable pull-ups overnight for a few more months, but these were only for the occasional accident that happened less than once per week.  We might have been able to complete potty training earlier, but there wasn’t much urgency, as we were only really dealing with the occasional wet nappy at that point.

Baby Led Weaning

There are a range of different approaches that could all be described with this label, and as with many things, the most extreme versions can create their own set of problems.  Despite liking the general philosophy of consent based parenting, the main issue that we had with "gentle parenting" and “child led” approaches is that many people seem to take them to extremes.

There are many skills and behaviours that children need to learn in order to be functional people.  In our view, it is not good enough to just sit back and wait for them to express interest - you have to generate the interest yourself!  Getting a child to do something when they aren't interested is often difficult and counterproductive, putting them off even more, therefore it is important to make the activity fun and appealing.

We were planning to start weaning at about 6 months old, but our baby ended up being very interested in food, and started grabbing and tasting things that were on our plates at just over 4 months.  They didn’t really start ingesting significant quantities until around 6 months, but by this point their dexterity had improved dramatically.

The main tenets of “baby led weaning” that we embraced were:

• They eat the same thing as you - no need to prepare food separately, you just have to avoid too much salt and preferentially chop things into stick shapes that they can get their fist around.  They therefore get used to eating as much variety as you do.

• They eat at the same time as you, at the dinner table - they don’t feel like they’re being watched over while they eat, they can just copy what the adults are doing.

• It doesn't matter how much they eat - it's about the experience and the enjoyment.

This made life easy - no blending everything into a mush, no cooking two separate meals every mealtime, very little spoon feeding.  I think that we were very lucky to have a child that was keen on food, but I don't think we'd have changed much if they weren't.

We weren't too obsessive about avoiding sugar, for example our baby ate quite a lot of fruit, but we tried to steer clear of desserts until age 1, and only occasional small portions thereafter.  This had the unexpected benefit of making them take Calpol very easily.  A couple of different doctors have made the comment that "they take medicine well - they must not eat much sweet stuff".

We also weren’t that extreme about things being "baby led" - if they didn't want to eat something, that was fine, but we still kept offering it at mealtimes, and gently encouraged them to at least try it.  Often we would find that a few weeks after trying and disliking something, they would suddenly start eating it for no discernible reason.

Having a Flexible (and Late) Routine

Most parents we encountered had quite rigid schedules for sleeping, naps and eating, and many set quite early bedtimes despite not enjoying the very early mornings.  We wondered why this was, as the rigidity was often quite limiting and felt unnecessary; while the early mornings sounded unpleasant and seemed easily resolved by a later bedtime, despite people clearly not taking this option.

Several people we spoke to considered this rigidity to be the only way that worked, but we decided to see whether we could avoid these limitations, and we found that we could.  It was a lot more pleasant - naps/food were not "expected" at certain specific times, so we could fit them in more easily around other activities that we did during the day.  This also made it easy to adapt to changing requirements (e.g. 2 naps down to 1 nap wasn't a huge adjustment - two 2hr naps became two 1.5h naps, which then became one 2.5h nap etc.).

Due to eating dinner at the same time as us, our baby generally had a bedtime of between 21:00 and 21:30.  This caused us no issues, and by 6-7 months old, it resulted in a usual waking time of 8:30 - 9:00.  Many people would consider this a very late bedtime, but the baby was getting the same number of hours of sleep as other babies their age - it just meant that we didn’t get woken up at 6am every day, which was glorious.

Once we were no longer both on parental leave, this late bedtime had another huge advantage.  Arriving home from work after your child has already gone to bed, whilst regrettable, is a pretty normal experience for many people.  Due to the later schedule, in the almost two years since we returned to work, I think this scenario has only happened once or twice to each of us.

One justification that we heard for not having such a late bedtime was that “they’ll just wake up early anyway, and then be grouchy all day”.  This didn’t gel with our experience of travelling, after all, if you’re waking up at the same time each day, and that isn’t the time you want to wake up, that is just jet-lag.  As with many adults, the process of overcoming jet-lag can take a couple of days, but after a couple of days of broken sleep, you all settle into a new routine.

When travelling, skipping a nap was a good way to bring bedtime forward by a couple of hours, and a later, longer nap was a good way to push bedtime back by a couple of hours.  If our baby woke up in the middle of the night, they were generally still pretty tired, so comforting them back to bed would usually take less than half an hour.  The same techniques we used to help our baby overcome jet-lag were useful in ensuring that their sleep cycle was properly aligned with the 21:30-8:30 sleep window.

Floor Bed

We encountered this idea through researching Montessori methods, which in general seemed quite well aligned with how we wanted to approach things (e.g. treating the child as an independent person, and being mindful of their desires and opinions - Philippa Perry’s book was very helpful for this too).  We definitely haven’t been following Montessori methods to the letter, as they can be quite prescriptive, but we used it as inspiration, and Simone Davies’ books “The Montessori Baby” and “The Montessori Toddler” were very helpful for this.  It also has some clashes with other approaches that we were using, which I will briefly detail.

In conflict with EC, the Montessori approach says that you shouldn’t disturb playtime, as play is work, whereas EC suggests that you offer potty as soon as you see a cue.  We tended to interrupt play if they deliberately cued or were distressed, but were more relaxed about more subtle, non-deliberate signals.  With offering the potty at transitions between activities, we found that they developed the ability to hold it in until they were next offered the potty (within reason).

In conflict with BLW, the Montessori approach suggests having babies at their own tiny table, whereas BLW tends to have them at the same table as adults, able to watch adults eat, and eat the same things as the adults.  We tended more towards BLW, as eating with us was more convenient and encouraged interest in more adventurous foods.

Interestingly, the idea of a floor bed seems to be one of the less popular Montessori concepts, possibly because of how unusual it appears at first glance.  Child-proofing an entire room, and setting it up for them to have free reign within it, does make it look very different to what you might expect from a traditional baby’s bedroom!

We moved them from a bedside cot to their own room with a floor bed at about 6 months old.  In the early days of this, we would tend to go in whenever they stirred, so that they wouldn’t feel abandoned, but we found that they very quickly adapted to the change, and quite liked the independence.  A video monitor was invaluable, as this enabled us to keep an eye on what they were doing.  Rather than needing our help to be let out of a crib, they were free to explore, and this led to them being much less likely to cry when they woke up in the morning.  It also meant that we didn’t have to lift them out of their cot, which meant much less strain on our backs as they grew heavier.  

When we first moved them to the floor bed, we found that they would often roll out, so we used some lengths of pipe insulation (similar to a pool noodle, but much cheaper and narrower), under the bed sheet, creating a slight barrier to avoid accidental rolling.  A few times we found that they had gotten out of bed in the middle of the night, and were asleep elsewhere in the room, but this wasn’t really a problem - we could usually go in and gently move them back into bed.  After a couple of months, they started to crawl, and they started heading back to bed themselves when they awoke in the middle of the night (sometimes falling asleep before they made their way all the way onto the mattress).  At this point we removed the roll barriers, so that they could get back into bed more easily.

From quite early on, our child would often wake up and play independently for up to 20 minutes before getting bored and demanding our presence.  This was great for gentle starts in the morning.  Not feeling trapped in a crib also made them much more inclined to go to bed.  I can imagine that if you were to dislike your bed, you would be less likely to volunteer to go there, but by 11 months old, our baby would sometimes take themselves to bed if they were tired enough!

One further benefit was that the floor bed helped them to get used to there being a drop at the edge of the bed.  After we removed the roll barriers, they initially rolled out of bed at some point on most nights (though this didn’t usually wake them).  This quite quickly became more of a rarity though, and by age 2 we were comfortable putting them in a standard bed, raised off the floor.

Both Parents Working Part-Time

Aside from taking parental leave together, this has had the biggest impact on how we live our lives, and I am very happy to strongly recommend it to anyone that will listen.  Both my partner and I used to work 5 days a week, as is the norm, but on returning from our 6 months of shared parental leave, we both went down to 3 days a week.  After all, 6 months old is very early to go into full-time childcare, and neither of us wanted to stop work completely.  Thankfully in the UK, companies have to have a “good business reason” to deny such requests, so we were able to clear this with our respective employers before the baby was born.

My partner works Monday to Wednesday, and I work Wednesday to Friday, which means that every week we each have 2 days looking after the baby by ourselves, with weekends together as a family, and only one day on which we need to pay for childcare.  With only 1 day per week at a childminder, it isn’t too expensive, so we don’t feel like we are working just to pay someone else to raise our child, as people often feel when both parents stay in full time work.  Although we currently live a bit far from our respective families for it to be relevant, 1 day per week is a small enough amount that some people might even be able to find family or friends that can help, without it being an unreasonable ask.

From an egalitarian perspective, this approach works incredibly well when contrasted against the model of one working parent and one stay-at-home parent.  We both share the responsibility for child rearing, being able to appreciate the difficulties of both childcare and work.  This allows us to share different approaches with each other, and support each other, as we are not living in totally separate worlds.  In a more traditional situation, with a stay-at-home parent, it is very easy for the parent in employment to generate frustration by simply offering their opinion, or trying to help.  After all, it is difficult for this to not come across as “I know better than you, despite having hardly any experience”.  As equal caregivers, suggesting alternative approaches to each other is much less likely to generate frustration, and those suggestions are much more likely to be actually useful.

Among other things, most relationships are built on a foundation of shared experiences, which may be why many couples find that the first years of raising a child takes a significant toll on their relationships.  If one of you opts to be a stay-at-home parent, you will start to have very different life experiences from each other.  Further to this, if you aren’t the one doing a job, it is very easy to fail to appreciate how much hard work it can be.  By both getting the experience of looking after our child, we are able to share in the experience and bond over it, as well as being able to appreciate the difficulties that the other is having.

By spending 3 days out of each week at work, we are both also able to maintain our respective careers.  We both get to interact with other adults regularly, avoiding the stay-at-home pitfall of chronic loneliness and ego death.  Neither of us will have a gap on our CV or in our professional development, and whilst we might find that our progression slows down relative to full time workers, we are both sharing that hit as equally as we can.  Further to this, neither of us is the default "primary caregiver" - both of us are the caregiver on our respective days.  Some employers have an issue with parents that are part-time workers, because they often have to leave early when their child is sick, but this isn't the case here, as on work days, the other parent is the caregiver.

I have heard from several people that (for various reasons) work part-time at 4 days per week, that the 4-day week is quite problematic.  Employers tend to expect the same amount of work from you as if they were paying you for 5 days, and by working late, this is actually possible to deliver.  As such, it can be difficult to enforce a boundary with the employer, that you should in fact be given less work, and not have to work late to compensate.  A 3-day week does not have this problem - with the best will in the world, a full time job cannot be crammed into that timeframe, so employers have to adapt their working procedures around it.  Of course, they may use this as a reason to deny the part-time request, or just make your life difficult, but more and more employers are coming to terms with part-time working, so it’s probably worth a try.

For weaning and sleeping specifically, there were distinct positives to the father having regular 1-on-1 time with the baby.  Having breastfed the baby, weaning was much easier on the days mum wasn't around, as the baby has less expectation of being breastfed.  Similarly for sleeping, in some circumstances it was easier for dad to settle the baby, as there was no expectation of being fed to sleep.

Aside from the egalitarian angle, there are a few other advantages that we have found to this approach.  For families in which both parents return to work, separation anxiety can be an issue, and some babies start waking in the night as a result.  By avoiding full-time childcare, we didn’t have to deal with this - our baby adapted to 1 day per week at a childminder in hardly any time at all, as they very quickly realised that it was only for a single day at once.  The multiple different approaches used between dad, mum and the childminder were also very useful in reducing blind spots.  We were all much less likely to miss something, as we all had different thought processes and experience.

No Screen Time

One thing that we were quite vigilant about was avoiding screen time.  This is another controversial topic, as I think it is something that many people feel judged about.  I want to make clear that I am not passing judgement on anyone that gives their kid screen time - it is a personal decision, and it would have been much more difficult for us to stick to if we weren’t sharing the effort by working part-time.

While several studies have shown that “excessive” screen time can negatively impact executive functioning and sensorimotor development with long term effects, it isn’t always clear what counts as excessive.  We did however come across various anecdotes suggesting that any kind of regular screen time has some negative impact, and some people have found that weaning their children off screen time helped them to sleep better and develop better self-regulation and patience.  As such, we made significant efforts to avoid screen time, and used it only as a last resort a couple of times, watching one or two episodes of something when 1) we were on a long-haul flight and 2) we all had COVID and could barely function.

One thing that seems very clearly inversely related to the amount of screen time they get is a child’s ability to play independently.  By avoiding the promise of instant gratification that a screen provides, we found encouraging independent play much easier.  Ultimately, a child without access to a screen needs to learn how to entertain themselves.  To encourage independent play, we tried to leave them to it some of the time - finding things that would entertain them, and then leaving them to play with the toys by themselves.  Another quite Montessori approach.

Whilst this may have made life a bit more difficult in the early days, for us it definitely paid off in the long run.  Having learned to play independently, and not being used to screens being on offer, they generally don’t make demands to watch anything.  They are also able to sit in restaurants and be entertained by the food, a toy or other people, without needing a screen.

Books and Letters

We have tried hard to make words and numbers interesting and exciting.  As mentioned above, it’s difficult and counterproductive to get a child to do something they’re not interested in.  Therefore we have read books to our baby from the start, and engaged with the content in a way that makes it exciting (“look, it’s a fish - blub blub”, etc.).  This has engendered a love of books in our child, as intended, which is a good sign for future learning.  There is nothing particularly new or controversial here, as reading to your child seems to be one of the only things that has been conclusively shown to improve educational outcomes in children in a statistically significant way.

Having succeeded in generating an enthusiasm for books though, we have been able to take this one step further.  We were given some letter/animal fridge magnets around age 1, which we mainly played with as an after dinner treat (since they were in the kitchen).  Having looked into Phonics a bit, we tried to be consistent in our use of the letter sounds for the letters (rather than using the letter names), and this turned out to be one of the best toys we had.  It really sparked an interest in letters, and before long we had stuck up a few letters from a phonics chart in the kitchen too, which our baby loved pointing at and trying to make the sounds.

It is worth noting that all of this was driven by the enthusiasm and interest that they showed - we weren’t sitting there and forcing our 1 year old to pore over phonics charts.  We just made the letter magnets seem exciting, and they started noticing letters when out and about as a consequence.

Shortly before age 2, they were able to recognise and sound out every letter of the alphabet.  We looked into the next steps in phonics, which was not entirely trivial, as most resources either stop at this point, or are targeted at parents supporting the learning that is being undertaken at school.  Thankfully a friend that was a teacher was able to point us in the right direction, and we were able to start on digraphs and dipthongs.

By their second birthday, we acquired a much bigger set of fridge magnet letters (made of smaller letters, without the animal associations).  These probably wouldn’t have been of much interest before, but by this point, letters were interesting to our toddler in themselves.  These immediately jumped to being one of the favourite toys (behind only the favourite teddy and perhaps the duplo chickens…).  After only a couple of months of playing with them (“dad, spell edamame on fridge”), they’re able to recognise some 3 letter words like cat, mum, fix, etc.

Numbers have been similar - lots of reading number books, and counting objects.  Our toddler is able to recognise all of the digits from 0 to 9 (still occasionally gets 6 and 9 mixed up, but gets it right more than half the time).  I say this not to brag, but to assert that it is possible.  The number of people I have encountered that thought that what we were doing was pointless is staggering.  “Oh, they’re far too young to recognise numbers yet” - well yes, that was true at one point, but by seizing the opportunity to show them, every time they expressed an interest in a number book or a letter magnet, we were able to keep them interested enough to learn.  The attitude of “they can’t do it yet, so don’t teach them” is one that I personally find quite bizarre - after all, how do you expect to teach something if a prerequisite to teaching the thing is them already knowing it.

What is more, this process is a lot of fun.  There is something truly wonderful about showing someone something new for the first time, and watching it sink in.  Every success is exhilarating; every time they recognise something and are able to apply it outside of the environment in which they learned it, is a rush of adrenaline.  This is something that we are only able to do because of the way that we have set up our lives - part time working, which allows us to use minimal outside childcare, whilst also allowing us both to maintain our careers and not get burned out being a carer.  This means that most weeks we come to our 1-on-1 days reinvigorated, with excitement, energy and new ideas.

As mentioned previously, I wasn’t expecting to enjoy the first few years of having a child at all, but I can honestly say that the way that we’re approaching it has been far easier and more fun than I would have dared to dream.  If someone offered me 10x my salary to come back and work full time, I would have to respectfully decline - there is more to life than work.

“No one on his deathbed ever said, ‘I wish I had spent more time on my business.’”

Arnold Zack in a letter to Paul Tsongas

It's a good job that we feel this way really, as our second was born just a few weeks ago. When I said "we will definitely be doing the same thing next time", I really meant "we are doing this again, right now". Time will tell whether our various approaches will be as successful a second time around, but so far I am reasonably confident that they are sufficiently flexible that we can make them work for another different child.

Within this context, the idea of “share buybacks” seems shady - rather than paying the shareholders their due, the company instead embarks on some back-room market manipulation, spending the shareholders cash to prop up the share price and net the executives a bigger bonus.

This narrative, that share buybacks are done to enrich insiders at the expense of other shareholders, and that dividends are fundamentally different, better, simpler and more honest, is incorrect and unhelpful.  It is an overly divisive way of framing a fairly technical choice, that leads people to favour a more obscure system.  In this post I hope to offer a viewpoint that explains the following:

1. They are basically accomplishing the same thing, but dividends are a more confusing way to do it

2. The ways in which they don’t result in the same outcomes are artificial, arising from legislation treating them as though they are not the same

3. Any accusations of insider shenanigans can apply equally to either, and many claimed problems with buybacks are complete non-issues

4. Buybacks are just better than dividends. As well as being more complicated, dividends reduce choice and possibly encourage short-termism

Keeping People Happy

Given the fact that many consider dividends to be the fundamental reason behind investing in the first place, in order to make an argument about their equivalence to buybacks, we need to dig into a more fundamental concept.  What are shares for, and why do we buy them?

A share gives you part-ownership of a business entity.  Owning a share means that you own a tiny proportion of everything that makes up the company - its physical assets, its bank accounts, and any future profits or investments it might make.  If the company ceased trading and liquidated its assets, once all its creditors had been paid, you would be entitled to a proportion of the remaining money.  Of course, this rarely happens outside of corporate bankruptcy, in which the company is in dire straits and cannot afford to pay its creditors, which usually means that there won’t be much left (if anything) for the shareholders once all debts are paid.  In principle though, you could wind up a company and liquidate its assets, and it is this value, combined with an expectation of how this value might grow in future that determines what people are willing to pay for a share.

When the stock market was a new idea, it was a wild-west out there.  Some companies were just pyramid schemes, relying on a “greater fool” to buy shares from existing shareholders, until some people were left “holding the bag”.  With weak regulation, and investors that didn’t have much experience (because no-one had much experience when the stock market was new), companies needed a way to distinguish themselves from pyramid schemes.  In this environment, paying dividends gave companies legitimacy.  Owning a share that paid regular dividends gave you a demonstrable financial benefit without having to sell the share to someone more gullible.

In modern times, there is a plethora of regulation - companies publish regular financial statements, and securities fraud is treated and policed very seriously.  This allows people to have a much greater degree of confidence in the financial status of their investments, reducing the need to demonstrate legitimacy through dividend payments.

Instead of paying dividends, a company with a significant amount of cash in their bank account may of course choose to invest their money in other growth opportunities.  This would be done with the aim of increasing the net worth of the company, and therefore increasing the share price.  If they do not currently have a suitable investment opportunity however, it would still be in the company’s interest to return this unused cash to the shareholders somehow.  This is because sitting on cash is actually expensive for companies.

Burning a Hole in Your Pocket

The last sentence might sound odd.  Surely sitting on cash doesn’t cost anything, after all as individuals, many people stash money away in their bank accounts, and this is considered prudent - “saving for a rainy day”.  Of course, having a certain amount of cash is useful for companies too - if you can’t pay your employees after a bad month of sales, you aren’t going to be in business long.  This desire to have a bit of a cash buffer is very reasonable, but the bigger the buffer you have, the more expensive it is.

The idea that it is expensive to sit on a large cash balance comes down to the idea of “cost of capital”.  Banks loaning money to a company charge interest, which provides them with a return on their investment.  This interest is referred to as a cost of capital, as it is a cost the company must pay as a result of the capital investment the bank provided.  In much the same way, shareholders expect a certain return on their investment - the capital they contribute isn’t free either.  In fact, this expected return is usually higher than the return a bank would make on a loan, as the bank is taking a lower risk - they’ll get their money back first if the company goes under.

This means that every pound or dollar of capital a company has is costing them - either in terms of interest to a bank, or expected return to a shareholder.  If a company isn’t growing fast enough relative to the amount of capital invested, the share price will fall, and the shareholders will be unhappy.  If a company has assets that it isn’t using, they are not contributing to the company’s growth, so their associated cost of capital is just a drag on the business.

The cost of capital forces companies to strive to be as lean as they can reasonably manage - maximising the growth they can achieve whilst minimising the capital they require to achieve it.  Whether it is cash languishing in their bank account, or a factory standing idle, these represent an unnecessary cost that can be done away with.  This is one of the main reasons why companies return cash to their investors - it reduces their cost basis.  The investors can then take this money and invest it elsewhere at a higher rate of return than the company could otherwise have achieved with it.

With this background, we can start to explore the impact of the different ways a company might dispose of its excess cash.

1a. Accomplishing the Same Thing in Different Ways

The obvious way that a company could return cash to its investors is through dividends - just paying a bit of the excess money to each shareholder in proportion to the number of shares they hold.

If a company with a share price of £100 and 1 million shares (therefore a market capitalisation of £100 million) were to have £5 million of cash in excess of what they needed, they could pay a £5 per share dividend.  This would reduce its market capitalisation to £95 million, and therefore the share price of all 1 million shares would drop to £95.

Note: because dividends can’t easily be paid to all shareholders instantaneously, a work-around is used.  At a particular point in time, rather than paying the dividend itself, it is instead determined who owns the shares and should therefore receive the dividend (the day before the “ex-dividend date”).  The payments to these people can then be made over the next few days, regardless of who buys or sells in the meantime.

This share price drop on the ex-dividend date is well documented - it is a result of the stock market being a highly efficient price determination mechanism.  After all, if you own something worth £100, that you know has the capability to pay you £5, once it has paid you the £5 it must be worth £5 less.  If it were worth £100 both before and after paying the dividend, someone could have bought it from you before the dividend was paid for £101, and sold it back to you after the dividend for £99, and still made a guaranteed £3 profit.

Of course, real life always makes things slightly more complicated - share prices fluctuate all the time, so in the instant a share’s ex-dividend date is reached, a stock might drop more or less than the value of the dividend, because other factors affecting the share price are also contributing to the movement.

Another way that a company could return cash to its investors however is through a share buyback - the company could use its cash to buy shares on the open market (or from shareholders directly), reducing the number of shares in circulation.

If the company above were to use its excess cash to perform a share buyback, instead of paying a dividend, it would still have £5 million of cash to pay out, which would therefore still reduce its market capitalisation to £95 million.  Rather than paying an amount to every shareholder, thereby reducing the value of each share, it would instead simply buy 50,000 of its own shares, reducing the total number of shares in circulation to 950,000.  Each share would therefore still be worth £100 to all of the shareholders that didn’t sell.

Under this approach, even if the market for the stock isn’t particularly liquid (i.e. the number of buyers and sellers is low, meaning that if you wanted to sell, you might have to wait some time, or accept a lower price in order to sell quickly), the company can periodically buy people out of their shareholdings.  People can rely on the company itself to be the “greater fool”, allowing them to exit their position.

With the dividend, everyone had their shareholding reduced by 5% whether they liked it or not, so anyone that wanted to maintain the amount they had invested would now need to reinvest their dividend - buying 5% more shares to replenish their portfolio.  On the other hand, with the buyback, anyone that wanted to convert 5% of their shareholding to cash could simply have sold 5% of their shares.  In both situations, the company has transferred £5 million of cash to its shareholders - the only difference is who had to take an action, and who did not.

There is no difference in value between share repurchases and dividends.

McKinsey & Company

1b. Individual Perspective

We can now imagine two different people, Amy and Ben, each initially with 20 shares.  Amy wants to simply hold the shares and watch them grow, while Ben wants an annual 5% cash income from their shareholding.  With a stock that pays a dividend, Ben has to do nothing - his 20 shares are now worth £1,900 and he has the £100 of cash he wanted.  Amy can use the £100 to buy another share (technically she would need to buy just over 1.05 shares, as the shares now cost £95, but some platforms allow fractional share ownership, so we can gloss over this), to maintain her £2,000 shareholding.

With a share buyback, this time it’s Amy’s turn to do nothing - she doesn’t want to sell her shares, so can keep all 20, which are still worth £100 each.  Ben can sell one of his shares to give him the £100 cash, leaving him with a £1,900 investment (this time consisting of 19 shares each worth £100).  In fact, Ben doesn’t have to sell his share while the company is implementing their buyback - he can sell his share whenever he wants to.  In both scenarios, Amy is left with a £2,000 investment, and Ben has a £1,900 investment and £100 in cash.  The exact number and value of the shares isn’t particularly relevant.

Of course, the difference in the number and value of the shares does affect some things.  When a dividend is paid, the share price changes, so a graph of the share price will reflect this movement.  This article is a good demonstration of the misleading nature of dividends - just looking at the chart of the share price, you could be forgiven for thinking that Verizon has performed very poorly in comparison with the wider market.

In order to get a true reflection of the actual returns you would have received from such an investment, we need to do some sleuthing to find what dividends were paid, and then some number crunching to calculate the returns with dividends reinvested.  Helpfully, many websites do some of this analysis for you, and a “returns with dividends reinvested” option is often available.  This isn’t universal though, and doesn’t completely remove the potential for confusion.

The flip side of this, is that with buybacks, a company will slowly be reducing the number of its shares in existence, and if it is remaining a similar size or growing, this means that the individual shares will be getting more and more valuable.  Very expensive shares are quite illiquid, as most platforms deal in integer numbers of shares (though as mentioned above, this is slowly changing).  The requirement to invest a large minimum amount in a company will put off some investors who don’t have the necessary funds or are unwilling to commit such a large proportion of their net worth.

The solution to this is to perform stock splits - to keep the share price manageable, the company can for example decide to replace their 1 million shares worth £100 with 2 million shares worth £50 each.  This is a very common and uncontroversial action, for example since being listed publicly, Microsoft has undergone 9 separate stock splits, and Exxon-Mobil has undergone 5.  There is virtually no impact to investors of performing a stock split - you end up with more shares that are worth less, leaving you with the same value of investment.  Interestingly it has been a deliberate decision by the board of Berkshire Hathaway to never split their stock, in order to discourage short-term investors, resulting in their share price being around $380,000 in March 2021.  If you look at a graph of Microsoft’s share price, the price shown in December 1986 is only $0.17 - this was not actually the case.  The price of one of Microsoft’s current shares would have been $0.17, but only because the combination of stock splits since 1987 has split one share into a whopping 288 shares.  This means that the price of a single share in Microsoft in 1986 was actually around $49, and if you bought a single share in 1986 for this price, you would now own 288 shares worth over $66,000.

To continue our example of Amy and Ben, we could imagine the company that did a buyback performing a stock split to keep everything even more similar between the two cases.  To keep things as similar as possible, the company could do a 20-for-19 split (in which 19 old shares become 20 new shares).  This would be unusual, as it would have a fairly minor impact (most splits are 3-for-2, 2-for-1 or higher, for example Apple’s 2014 7-for-1 split), however for the purpose of this example it is informative.  The split shares would be worth £95 each, down from £100, and Amy’s 20 shares would become 21.05 shares, while Ben’s 19 shares would become 20.  This then perfectly matches the end state where the company paid a dividend instead.

2. Artificial Differences

The fact that the end result of a dividend payment and a share buyback are the same in principle, doesn’t necessarily mean that laws treat them the same.  Paying a dividend usually means that the income people receive is taxable - even if they then immediately reinvest it.  Equally, selling a few shares will generally incur Capital Gains Tax, so if capital gains are taxed differently to income, receiving a dividend may be more or less tax efficient.

In the UK, this is an unhelpfully complicated thing to consider.  Your first £2,000 of dividends and £12,300 of capital gains are tax free, then if you are a basic rate taxpayer dividends are taxed at 7.5% and capital gains at 10%, while if you are a higher rate taxpayer dividends are taxed at 32.5% and capital gains at 20%.  This means that depending on your other income, it could be more or less tax efficient for you to have a stock pay a dividend vs. just selling the stock.

Given that the two approaches give the same result from the perspective of the company and the shareholders, in my view the government shouldn’t tax them differently.  If a government chooses to treat them differently however, companies can hardly be blamed for picking the one that reduces the tax burden for their investors the most.

Aside from tax, there are also accounting considerations - generally speaking companies are restricted from paying dividends if they don’t have enough profit.  It stands to reason that they shouldn’t be paying money back to shareholders, if they haven’t actually made money!  Share buybacks are more ad-hoc, and have therefore not yet been regulated to the same extent, leading to some companies borrowing money in order to do a share buyback, despite being loss-making.  This is the kind of behaviour that could give buybacks a bad name, so it shouldn’t be a great leap to suggest that similar regulation should be in place to restrict buybacks based on profit.

3. Insider Shenanigans or Just Manufactured Outrage

We are still left with the question of whether buybacks could be used to manipulate the share price of a company.  Do share buybacks really funnel money into the pockets of insiders?  Of course, if there is any way for people to line their own pockets, you can guarantee that someone will try it - I am not suggesting that there aren’t new and innovative ways for executives to commit securities fraud.  I’m simply pointing out that all of the ways that people have so far suggested that buybacks are terrible either don’t hold water, or apply just as easily to dividends too.  Let’s run through the popular ones:

EPS manipulation

This article states that “Buying back shares is a common technique to artificially increase earnings per share”.  This is technically true, but not as meaningful as you might think.

Generally, a company must spend its retained earnings in order to perform a buyback.  If it is spending its earnings to buy back shares, clearly its total earnings per share can’t increase.  EPS however only refers to earnings in the current year, rather than total retained earnings, and it is indeed currently possible for a company to use historic retained earnings to fund a share buyback, without impacting current year earnings.  This yields an obvious possible regulatory solution – if people consider this to be a genuine concern, we could simply require that buybacks come out of current year earnings first, before they can use historic retained earnings.  This is however not something that I am advocating for – the change in EPS as a result of a buyback is just not that big of an issue.

Companies have to spend cash to purchase the shares; investors, in turn, adjust their valuations to reflect the reductions in both cash and shares. The result, sooner or later, is a canceling out of any earnings-per-share impact. In other words, lower cash earnings divided between fewer shares will produce no net change to earnings per share.

Investopedia - 6 Bad Stock Buyback Scenarios

Once shares have been bought back, of course any future earnings will result in higher earnings per share, because there are fewer shares.  This is both obvious, and not a problem – the company’s cost of capital has been reduced, so it is more streamlined, able to provide a higher rate of growth for the remaining capital invested.  Why shouldn’t board members get a bonus for reducing costs and increasing the rate of growth?

The EPS concern is therefore mainly with the current year’s earnings to date, however this can be looked at from the same perspective.  Had the board decided to do a buyback using historic earnings before the start of the current year, this wouldn’t be an issue, as per the previous paragraph.  It is only the fact that they held onto the earnings until later, that causes accusations of foul play.  Should executive bonuses be lower if they have been conservative with their cash – waiting until they are confident that they don’t need it before returning it to shareholders?  This is a fair question, and one that the company’s Remuneration Committee would want to consider, but looked at from this perspective, it is no longer quite as clear cut as the situation at first seemed.

Executive bonuses are something that a considerable amount of thought goes into.  There are entire departments of consultancy firms that exist to advise companies on how to structure executive pay.  In most cases, it is simply not the case that the possibility of “EPS manipulation” hasn’t been factored in.  It is likely to have been considered in one of a few different ways:

• The possibility of buybacks could already be included in the performance calculations, allowing executives flexibility around buying shares back

• The bonus payments could be calculated based on a “synthetic” EPS basis that remains unaffected by share buybacks

• An irregular or large buyback could trigger a review by the company’s Remuneration Committee, in order to assess whether the existing executive pay structure is fit for purpose

• The executive's remuneration may not use EPS as a metric at all - there are many other metrics that can be used to more accurately track performance

This compares very naturally with dividends – the other way the company could have disposed of its excess cash.  Some companies have executive bonuses that are tied to keeping dividend yields above a certain level - if instead of a buyback, the directors had decided to pay a dividend in order to hit their bonus targets, would we be criticising them?  It doesn’t matter – dividends and buybacks do the same thing, so either both are bad, or neither are bad.

Buying back stock options

The same article complains about this in the very next paragraph.  Executives and other company employees are often paid bonuses in options (the right to buy shares at a later date at a particular price - the “strike price” of the option).  If the share price goes up, these options can be very valuable, as they give people the right to purchase shares at below the market rate, giving them an immediate profit when that right is exercised.  It is a true statement, that instead of buying back shares, companies can buy back these options, which is a direct transfer of money to “insiders”, but it is worth considering what the alternatives are.

Let us consider a company that issues 100 options to its employees, each of which confers the right to purchase a share in 1 years time, but at its current market value which is £50.  One year later, the share price has risen to £60, so each of these options could be exercised, allowing people to buy a share worth £60 for only £50.  At this point, the company could buy the options back for their intrinsic value (£10 each) - this seems to be what the article in question has an issue with, after all, this is a direct transfer of company money to insiders.

The thing is though, the deal is already done - the company has already committed to selling them the shares at a discount, by the nature of entering into an options contract with them a year ago.  They can’t just not honour it - that would be fraud.  They could of course refuse to buy the options back, and instead force everyone to exercise their option, buying a share for £50, which the employees could then hold on to, or immediately sell for that same £10 profit.  But where do these shares come from?  The company has to buy a number of shares in order to be able to then sell them on to the option holders.  The other side of an option contract that confers the right to buy at a particular price is the obligation to sell at that price, which the company has underwritten.

This therefore isn’t a problem with share buybacks, it is just a natural consequence of a company issuing stock options.  If you want to take issue with this mechanism, that’s perfectly fine.  The merits and drawbacks of stock options being issued as bonuses makes for an interesting discussion, but that isn’t this discussion.

Overt Buybacks

Another article complains that a company announcing a buyback can cause a spike in the price of its shares.  This “overt buyback” is seen as a cynical ploy to drive the share price higher, to allow insiders to profit.  Well, it is true that sometimes announcing a buyback can cause a company’s share price to rise.  This may be due to an expectation that higher demand will drive the share price higher still, or it may be that it triggers greater confidence in the company as it can part with some of its cash reserves, and remain comfortably solvent.

The thing is, this is exactly the same effect you see when a company announces a special dividend.  Despite the fact that nothing fundamental has changed about the underlying company, announcing a special dividend generally causes an increase in share price, just like announcing a buyback.  Again, if one of these things is bad, then both are.  I don’t hear any voices clamouring to ban special dividends, so there’s no reason to single out buybacks as some evil market manipulation tactic either.  Of course, as long as we’re being consistent, I don’t mind either way - if people think that both of these are indeed bad, I wouldn’t mind it if special dividends were banned alongside making buyback announcements.  Companies would just have to buy their shares back quietly and without fuss.  But wait!  The same article has a problem with that too...

Covert Buybacks

Ahh, I see - so it’s bad when companies tell you that they’re going to do a buyback, because that causes an increase in the share price, but it’s also bad when companies don’t tell you, because that allows them to buy their own shares more cheaply.  Oh the egregiousness of these dastardly executives! Pass the smelling salts!

Seriously though - the company is buying shares from people that want to sell them, at the price that they want to sell them at, whilst at the same time reducing their cost of capital by getting rid of cash they aren’t going to use.  Who is losing out here?  The sellers aren’t, because they were happy to sell at the market price.  The remaining shareholders aren’t, because the value of their shareholding won’t have been significantly impacted, and they now own a slightly higher proportion of the business.  This really is manufactured outrage.

Direct Buybacks

Buybacks can also be done a number of ways, and although one way is to do it on the open market, that isn’t always the case.  A direct buyback is an agreement to buy shares from particular entities or individuals, who may negotiate the price at which they sell. 

By doing a buyback this way, the company sometimes pays a premium above the market price for the shares, which could be seen as unfair to the other shareholders.  It can be beneficial to do this when there is low liquidity in the market, as the company can negotiate a price when the market is not reliable at determining the price for such a large order.

As mentioned previously, securities fraud is treated very seriously, so any buyback that overly favoured certain shareholders over others would receive significant scrutiny.  That being said, it is not impossible that a direct buyback could be performed inappropriately, overly benefitting an insider with a large shareholding.

With this being the case, open market buybacks are clearly preferable where possible, as they don’t permit such favouritism.  It would make sense to be more sceptical of direct buybacks, and the regulation should reflect this.

Excessive Volume or Liquidity Issues

One way that a buyback could legitimately be called manipulation would be if the volume of shares being bought was too large, dwarfing the usual order book, and driving up the price with demand temporarily far outstripping supply.  This could easily be managed however, with some very light-touch regulation.

Picking a fairly large and steady company as an example, Costco Wholesale Corporation (COST) has a market capitalisation of $140bn and a share price around $320, meaning they must have around 440 million shares in existence.  If they had $7bn of cash sloshing around, that they wanted to give back to shareholders, this would be enough for a 5% dividend (16p per share).  Rather than paying a dividend, if they decided to do a share buyback, this would be the equivalent of buying back 22 million shares.  This sounds like a lot of shares, but without the need for an ex-dividend date, there is no need for these shares to all be purchased at once.  Over the past year, the trading volume has varied between 1m and 8m shares of COST per day - this means that they could spread the buyback over a couple of weeks, and trading would still be within normal parameters.

If share buybacks became the norm, and dividends were relegated to the history books, the somewhat ad-hoc and bespoke nature of buybacks would need to be harmonised and rationalised (in much the way that regulations have done with dividends).  Perhaps a daily restriction on the number of shares a company can buy, set at some proportion of the previous day’s trading volume would be appropriate.  Also if it became necessary, much like the SEC’s Alternative Uptick Rule for short selling, an equivalent restriction for buybacks could be used.  Only allowing a company to buy back stock on a downtick would ensure that a flood of buy orders from the company itself cannot cause a runaway spike in the share price.

Still though - outside of low-liquidity stocks and situations like a short-squeeze, buybacks don't really "inflate the share price" because share prices tend to have very elastic supply and demand. The big players in the stock market - market makers, hedge funds and the rest, all have a good idea of what they think the stock is worth, and will buy/sell shares if they think they are under/over priced. This means a very small change in the share price results in a huge demand - try offering to sell a share at the current bid price vs. at the current ask price, and see how fast your orders gets filled! Equivalently, it takes a huge demand to raise the share price a very small amount. Without the implication of market manipulation, the article about Boeing linked at the start of this paragraph could have equally been written about them paying too much in dividends, leaving them in a fragile situation with not enough cash.

4. Don’t Tell Me What To Do

Fundamentally, dividends are a forced action - in receiving a dividend, part of your shareholding is converted to cash whether you like it or not.  I am personally of the view that companies shouldn’t be telling investors what to do, or how to manage their money unless they’ve been explicitly asked to.

If someone wants a steady income stream, as pensioners might, for example - they can always sell stocks to generate income.  If such people didn’t want to have to actively manage their portfolio, there is no reason that a fund couldn’t act as a wrapper, managing the selling of an appropriate number of shares each month.  Not every investor in a company wants to use their investment as an income stream, so why force dividends on all of them?  It just results in people having to reinvest their dividends.

The pressure for companies to pay dividends could be harmful too.  Irrational though it may be, dividend payments generate excitement for investors, in a way that buybacks do not.  The flip-side of this, is that when dividends are expected, the lack of a dividend is disappointing to investors, where the lack of a buyback would not be.  A company that regularly pays dividends can find themselves in a position where they would like to invest money in the business, in order to grow the company, but they are strongly discouraged from doing so, as this would require them to “miss” a dividend payment.

Discouraging investment in the future of a company is fundamentally short-termist, and if a company feels that it can’t invest in itself for fear of upsetting its investors, that is a disaster waiting to happen.  Far better not to back yourself into a corner in the first place - if no dividends are expected, none can be missed, and investments can be made as needed, without fear of a market backlash.

One final area where dividends just make things more complicated without any discernible benefit is options.  As touched upon earlier, options give you the right to buy (or sell) shares at a particular price (the strike price) on a particular date (the expiry date).  If you buy a call option on a share currently priced at £100, with a strike price of £105 and an expiry date one year from now, this will give you the right to buy a share for the price of £105 in one year’s time, regardless of what its price actually is.  If the shares have increased to £110, you will be able to buy them for £105 and sell them at £110 for an immediate £5 profit, while if they have only increased to £105 or less, your option will expire worthless as there would be no benefit in buying the share at above the market price.

If you bought this option, and the share price of the company has increased to £110 over the last year, you might think you’re going to be making a profit, but what if the company pays a £5 dividend before you exercise your option?  Once the ex-dividend date is reached, the share price drops by about £5, leaving your option worthless.  If a share buyback had been done instead, there would have been no direct impact on the share price, leaving the option’s gain largely intact.  Of course, if you are aware of the risk, there are strategies to manage it, but this is just another thing you have to think about.

Conclusion

If you want a nice consistent cash payment, buy bonds instead.  Stocks are all about capital growth, and dividends obscure that.  In an ideal world, dividends would just be phased out in favour of share buybacks - they aren’t worth the hassle or the hype.  If you’re still not convinced, check out this video by InTheMoney, who expresses the point very succinctly.

The issue that I have with Milton Friedman, and the free-market capitalist policies that he championed is not with the fundamental validity of the ideas.  It is well established and demonstrable that investment is generally beneficial and free-markets generally allow for higher growth and lower prices.  The problem is instead with the extremes that he took these underlying principles to.  His philosophy was one of unyielding faith that the free market could do no wrong, and that any and all attempts to regulate the market are harmful.

Friedman’s recommendations were ultimately used as justification for much of the economic policy of Thatcher and Reagan, which are still highly controversial.  I would not consider myself to be anti-free-market, but I intend to present a counterweight to the dogmatic approach of Friedman.  Both capitalism and free markets can be hugely beneficial up to a point, but it is dangerous to pursue them to the exclusion of all other considerations.

Evolution Doesn’t Care

In order to illustrate the point I am trying to make, I shall take a diversion through a completely different topic: evolution.  Our understanding of evolution has progressed significantly over the past few decades, and it is now a fairly well understood example of an optimisation engine.

Evolution optimises for survival and propagation – if something is better able to survive, or able to propagate faster, it will outcompete other things.  There is a high degree of randomness in the environment – sometimes beneficial mutations die out due to bad luck, but if a beneficial mutation is likely enough, eventually it will overcome this variation and become dominant.  Evolution however does not specifically optimise for traits that we as humans may value, such as happiness, compassion or intelligence.  If compassion or intelligence helps an individual survive and propagate, an organism with that trait will be more likely to survive, and this trait will become more prevalent.  These qualities are not guaranteed to be beneficial from an evolutionary perspective though.  Evolution doesn’t care about what humans value. (For example, Cowpea Seed Beetles (Callosobruchus maculatus) engage in copulatory wounding - a behaviour that is truly horrifying from a human perspective).

Intelligence is useful for developing better tools, and this is helpful to the intelligent individual, however if anyone that sees the tool can copy it, the additional intelligence that allows them to develop improvements confers little lasting evolutionary benefit to the individual.  There are multiple theories that attempt to explain why humans have evolved to be so much more intelligent than other animals, but none of them rely on any sort of idea that intelligence is just some fundamentally good thing that evolution is optimising for.

Several of these theories rely on the idea that intelligence allows us to model and predict other humans' reactions to situations.  One theory is rather Machiavellian, in that our intelligence is the result of a runaway process in which humans would be more successful the more they were able to outsmart each other, leading to an intelligence arms race.  Another theory takes a slightly less misanthropic view - that collaboration is hugely beneficial to individuals within a society, provided there are no defectors, so the ability to reliably predict human behaviour allows better identification of defectors that would otherwise harm the group.  Either way, these theories suggest mechanisms in which a self-reinforcing cycle of increasing intelligence might be maintained.

These kinds of runaway processes can yield “useful” results (intelligence) or “pointless” results (peacocks’ tails).  Useful and pointless however are just human judgements - evolution “doesn’t care” about such things - it is simply mindlessly optimising for survival and propagation.

The Perpetual Arms-race

Obviously in the position Homo Sapiens is in now, we have an unprecedented capability to propagate (e.g. by leaving the planet), but evolution does not plan.  The eventual ability of space travel is entirely coincidental and did not confer an advantage to Homo Sapiens before it was fully manifested.  A different runaway evolutionary process - an arms-race between organisms developing toxins and anti-toxins would perhaps result in an extremely hostile world (consider the Amazon rainforest or perhaps the fictional xenomorphs in Alien).

Such arms races are still happening.  Just as dinosaurs were the dominant form of life before being wiped out, Homo Sapiens could be wiped out too – evolution doesn’t care.  Seeing the current state of the world with us on top, and assuming that we will stay that way is pure selection bias.

Humanity could yet be wiped out by flesh eating slugs or by a particularly virulent virus (for all the disruption that the Coronavirus pandemic is causing, things really could be so much worse).  For all we know, in another hundred million years, the planet could be dominated by the descendants of cockroaches.  These insects may or may not evolve intelligence, but human-level intelligence is only likely if there is an immediate fitness advantage to them that leads to a similar kind of arms-race scenario.

It is however exactly this kind of selection bias that makes people think that evolution is their friend, not some faceless uncaring optimisation engine.  They see the world and think “humans will continue to evolve, getting better, stronger and smarter”.  The flesh-eating slugs of the future wouldn’t care about an irrelevant species that died out millions of years ago, just as we don’t care about velociraptors today.  If we want to stay on top, we need to be aware of what is being optimised for, and find a way to satisfy that, staying on top whilst also satisfying our own desires of getting smarter, stronger, happier or whatever.

Treading this knife-edge between being a single-minded Machiavellian survivalist and a scholarly altruist is the great challenge of life.  The choice between sacrificing everything to the goal of propagating yourself, versus the desire to be a compassionate, artistic intellectual despite the likely outcome that you will be out-competed and eradicated by more ruthless players is a true conundrum.  If we sacrifice everything to propagate, what are we really propagating?  Surely there are some things that we have decided that we hold dear, that we are trying to propagate along with ourselves (like compassion, art or intelligence).  Equally though, if we hold too many things too dear – sacred cows that we cannot allow to be compromised; we risk being too inflexible – dying out, and having these ideas or qualities die with us.

When fighting disease, the optimisation engine works against us – antibiotics are great, but if used incorrectly some bacteria may survive, and the survivors will be the ones most resistant to the antibiotics.  They will then pass on their resistance, making the antibiotics less effective in future.  The way to fight disease is to act quickly enough to not give the optimisation engine time to work – hitting bacteria with a sustained barrage of antibiotics, so that a slight resistance doesn’t help them, and can’t be selected for.

There are equivalent problems with the recent proposed approaches to tackling malaria.  The female Anopheles mosquito (the primary vector for malaria) mates only once, so by releasing sterile male mosquitoes into the environment by the billion, many females will mate, have no offspring and die.  This seems like a fool proof plan to dramatically cut their population, and eventually wipe them out.  Thinking about it for a moment longer however, it becomes clear that if this plan is not executed globally in a sustained manner, wiping them out within a handful of generations, it will simply select for those rare female mosquitoes that mate more than once.  This strategy if executed imperfectly, will suppress their population for a time, then when we get bored, their population will boom, but filled with individuals on which this tactic will not work a second time – just like antibiotic resistance.

Optimisation engines are faceless and unrelenting – when they are optimising for something we want, that is good, when they are optimising for something we don’t, they have the potential to be very bad.  This is very much like the AI thought experiment about the dangers of Paperclip Maximisers, which seem to be doing a great job until they take over the world and turn it into paperclips.

Unfortunately we can’t simply “opt-out” of evolution and we ignore the reality of what is being optimised for at our peril.  We must make enough concessions to succeed without losing what we value in the process.  Getting ahead of the curve, and somehow diverting the unstoppable optimisation engine from going too far down a path we consider bad.

The Free Market

It is through this lens that we can view the free market: it is an optimisation engine.  This is an incredibly powerful force that often does exactly what we want - people freely trading with each other are able to exploit their comparative advantages to get more of what they want for less effort than they could have made it themselves.  These mutually beneficial trades increase everyone’s happiness!

Again though, we must be careful about exactly what is being optimised for: just as evolution is not optimising for intelligence, the free market is not optimising for happiness.  It is arguably optimising for profitability, and this does often coincide with progress, peace and happiness.  Indeed, if kept constrained within certain bounds, the free market is very effective at reducing costs and driving innovation.  The issue is that profitability is not completely synonymous with happiness, and happiness is important.  In optimising for profit, the following scenarios can occur:

• Marketing can convince people that their lives are miserable and inadequate, so that they need to buy things to make themselves feel better.  Without the marketing, people would be happier, but profitability is instead being maximised, so happiness gets thrown under the bus.

• Price gouging allows people or companies to profit from people in difficult or life-threatening situations, and whilst a certain amount of profit can encourage more players to enter a market (for example, getting food into a warzone is expensive and risky, so why bother if it isn’t going to be profitable), people that are sufficiently desperate are willing to take incredibly bad deals as they are unable to shop around.  This high profit environment is however a great opportunity for anyone that can corner it, which means that it would be in their interest to perpetuate the problem in order to make enormous profits for longer.

• Consolidation due to economies of scale can lead to oligopolies or monopolies, which are then able to extract supernormal returns due to the lack of competitors pushing their prices down.  Once in such a position, they are also often powerful enough to introduce barriers to entry that discourage anyone from trying to compete.  This is likely to be a natural attractor state for this kind of optimisation engine, so a completely unregulated “free market” that makes no attempt to avoid monopolies is highly likely to cease to be free, as it is taken over by monopolies.

• The drive for economic efficiency has led to an enormous amount of offshoring and specialisation - it is now evident that supply chains for many critical products are highly dependent on Chinese manufacturing.  This has led us to a geopolitical situation in which it is very difficult to challenge a country that is committing human rights abuses.  Repatriating the supply chains could take years, and without doing so, the costs of trying to sanction such a country are potentially ruinous.

When profit and human flourishing are not in alignment, we need a balance between ruthlessly optimising, and achieving our actual goals.  This can be government regulation, for example anti-monopoly legislation, marketing guidelines, environmental protections, etc.  As with evolution however, we cannot revolt without regard for what is being optimised for, or we will fail.

Mutual Existential Threat

Introducing government regulations that restrict companies in an effort to keep the market free and profit aligned with happiness sounds great.  Unfortunately though, the government doesn’t exist completely outside the system.  Any company that could profit from the removal of these regulations now has an incentive to disrupt the government.  Regulatory capture is a good example of this, in which companies use whatever tools and influence they have at their disposal to get someone sympathetic to their position installed in the relevant agency (e.g. polluters getting climate change deniers into an environmental agency).

Companies are therefore an existential threat to the government, as it is in their interest to try to capture the government and use it to their benefit.  Equally, through regulating the activities of companies and therefore reducing their potential profit, the government becomes an existential threat to those companies.  There is no way for the government to rise above the fray and insulate itself from these pressures, as it is made up from the same people as make up all of the companies that jockey for position in the market.

Some might say that regulatory capture is the fault of the government – if the government didn’t exist, how could companies lobby it?  How could they get regulations passed that benefit them and harm their competitors?  The answer to this is very simple – if there is no government to stop a company growing, gaining power and monopolising, they can simply become the government.  Perhaps at first this might be done at a local level, where they acquire enough power to be able to dictate what can and cannot be done in that locality, at which point they have become a de-facto local government.  All they need to do is to continue to expand, and the sky's the limit.

Effectively, there is always a government in one way or another.  A government is simply the power structure that places restrictions on what people can do:

• In dictatorships, the government is the dictator (and perhaps their generals).

• In representative democracies, the government is the group of people selected by the populace to govern.

• In anarchies, the government is whoever or whatever is the most powerful entity in a given situation, place and time.

If you reduce the size of government, and allow companies to grow larger and more consolidated, they become the power structure.  If this goes far enough, there is no reason that a company could not capture, subsume and replace the government entirely, making the CEO effectively the dictator, propped up by their “generals”, the key shareholders.  As long as the generals are kept happy, the dictator stays in power.

Going in the other direction, there are several governments that have reacted to the existential threat posed by companies in a free market by restricting the markets and companies heavily.  By crushing private enterprise out of existence, these governments may have avoided some of the excesses of free-market capitalism, but they have also forgone the huge benefits of the free market as an optimisation engine.  The government gaining control of a huge command economy is a hugely risky endeavour that leaves the country open to mismanagement and corruption.  A single failure can cause catastrophic economic collapse, as there is no backup - unlike a market system, the failure is not contained within a company that can go bankrupt without cascading further.

Regulation Within Reason

Ultimately, for all its difficulty, keeping the free market aligned with happiness and human flourishing is a job that only the government can do.  In my view this is therefore a key function of the government, requiring dedicated and diligent thought.  As such, contrary to the views of some politicians, regulations in themselves cannot be viewed as wholly good or bad - there are good regulations and bad regulations.

Some regulations are essential to keep the market free and avoid it from being misaligned, while others hinder the free-market optimisation engine with no discernible benefit.  Many of the benefits of the free market arise from situations close to perfect competition, in which there are lots of small companies competing against each other, driving the price down for the consumers of their goods.  It therefore stands to reason that most regulations that push the market towards this state are beneficial, and any that move it away from this state need careful consideration over whether their benefits outweigh the reduction in competition.

Often regulations are put in place that benefit incumbent companies or introduce barriers to entry for newcomers (e.g. state hairdresser licenses in the US).  Even regulations that at first glance seem costly to existing companies can be beneficial to them, by maintaining a bureaucracy that is difficult for new market entrants to navigate.  They will fight to preserve any barrier to entry that protects their turf.

An excellent case study for the risks of eschewing regulation entirely is the recent situation with Texas’ power grid.  Robustness was sacrificed for efficiency, by which I mean that actions that would have guarded against the problems being faced were not taken, as cost-saving was prioritised.  In a more competitive environment, the companies in question would have suffered for this lack of foresight, by losing out to their more prepared competition or new market entrants.  In Texas however, these companies were able to use their strong market positions to price gouge, passing on the cost of their shortsightedness to the customers.  Without a government willing to put in place regulations that would either enforce more competitive markets, or enforce robustness on the companies directly, the profit motive and the happiness of the people of Texas were not aligned.

The interesting problem is finding a system of government that is adequately resistant to capture, whilst also not interfering with the positive aspects of the free market too much.  A system of government that is adequately resistant to populism, whilst remaining democratic and representative of the people.  A system of government that is powerful enough to resolve the problems it needs to resolve, without being so powerful and overconfident that it tries to resolve problems it doesn’t need to.

If this sounds like a rephrasing of some of the thoughts in Meditations on Moloch, that is not a coincidence.  This balance between sacrificing too much to the optimisation engine, losing your values/happiness, and sacrificing too little, losing your freedom/life is very much the same theme that was addressed there.  I am however more optimistic.  It is not a battle that can ever be won with finality - it is an ongoing struggle requiring constant vigilance to ensure that our goals remain compatible with the reality in which we live.  That being said, humans are an intelligent species - as we come to better understand the rules of the game, we can learn where to exert pressure to subtly change the nature of the game itself.  Keeping the optimisation engines of both the market and evolution working towards our own ends as much as we can.

Here, I hope to reframe the discussion, explaining why the underlying concepts of capitalism and investment are good things in their own rights, and why those advocating for consumerism are actually wolves in sheep’s clothing.  Let’s not get ahead of ourselves though - it might help to think about some of the basics first.

What do we mean by capital?  From a finance perspective, capital is basically another word for money, but it is used in a specific way.  From a business perspective, capital is usually associated with a cost - it is either equity or debt, both of which are lent to the company with the expectation of making a return.  This is referred to as the “Cost of Capital”, and the returns that a company makes using the capital it has acquired is often known as ROCE (Return on Capital Employed).  From an accounting perspective, this capital is therefore a liability - money that it owes, either to shareholders, or to creditors (like banks).

Companies then spend this money on machinery, inventory, overheads and employees in order to produce something of value to their customers.  Everything a company owns, including its own profits are ultimately owed back to its shareholders and creditors.  If a company makes a net profit, these “retained earnings” are also owned by and owed to the shareholders, so they increase the amount of capital present.

The flip-side of capital is the assets that this borrowed money was used to acquire.  (Economists usually refer to these assets as capital goods or just capital, which they generally define as the "means of production", though I am not going to use this definition here, as it would become confusing.) These assets could have been purchased directly, or have been produced by workers that were paid by the company.  Ultimately, the capital present in a company is a monetary valuation of all of its assets (including any money it has sitting in its bank account).

So if capital is basically money that has been lent to a company, what actually is money?  This might seem like a bit of a silly question, but it is worth asking.  Now that we are no longer on the gold standard, money doesn’t have an intrinsic value like it once did.  When we used the gold standard, we were really just operating a barter economy in which everything got converted into units of gold before being traded for something else.  Money is clearly a measure of something that can be used to acquire goods and services, but what is it a measure of?

It is not a measure of “hard work” - many back-breaking jobs pay very little, while some other people do very little work, and accrue vast fortunes.  It can however be viewed as a measure of the “net amount of beneficial contribution you have made to the wider world”.  There are various ways for this metric to be subverted (worker exploitation, poorly negotiated contracts, taxes), which could have a big impact on individuals, but from a broad perspective, looking at the wider economy, this metric should be relatively reliable.  The amount of money you get for something (an hour’s work, or selling an item) is determined by its market value - how much other people value it.  Therefore the amount of money you have received should be roughly indicative of the amount of value you have contributed to the economy.

“Amount of beneficial contribution” is a bit of a mouthful, and is still not that well defined, so allow me to rephrase it.  I am going to use the term “wealth” for this; it may sound like I am using an odd definition of the word wealth here, after all someone with a lot of money is generally considered “wealthy”.  It is however helpful to separate these two concepts.  What I mean here by wealth is effectively just all assets except for money (defining money in terms of money wouldn’t be very helpful).

An Asset is a resource controlled by the entity as a result of past events and from which future economic benefits are expected to flow to the entity

International Accounting Standards Board Framework

Importantly though, for these purposes I mean for wealth to include things such as a person's education and experience that wouldn’t ordinarily be included by the formal definition of assets above. The control criterion means that employees and their expertise are not counted as assets - a company might pay their employees, but they do not control them in the strictest sense. An employee does control themself, so could consider their education to be their own asset, but this is usually just a colloquial use of a technical term.

At its core, wealth is the ability to either produce more assets or more happiness. This may just be a standard physical asset like a factory or some machinery, but can also be your own knowledge and experience. To attempt to avoid confusion, I am therefore using the term wealth, rather than using a non-standard definition of a technical term such as assets or capital.

By this definition, wealth is of course hard to measure, and its value is generally only really known at the point at which you sell your asset/your productive capacity/your time and expertise. If you own inventory of some product, or you own a factory that can produce that product, you could sell these for money; releasing it from your control, and contributing it to the wider economy. This amount of money is going to be roughly the amount of wealth you had before you sold it.

Likewise, if you sell your services either through employment or as a contractor, you are using your expertise to convert some of your time into wealth, for which you receive money (as you do not retain control of that wealth).  If, instead of employment, you just make things (perhaps as an independent craftsperson/artist), you could still be creating wealth, but it is very difficult to value how much wealth you have created until you sell your wares.

I. The Wealth Must Flow

Even though wealth is hard to value, it is much less abstract than money.  We usually view the economy through the lens of money, tracking its accumulation and its movements, as its easily quantifiable nature means that this approach yields very well to certain analytical methods.  Ultimately however, this lens can make some things in economics quite counterintuitive.  As an alternative approach, we could view the economy through the lens of wealth.  We can easily witness the production of wealth by people investing their time and resources in creating things that people want.  We can also see wealth being transferred around as goods change hands and factories change ownership.

Viewed this way, the flow of money around the economy is therefore a symbolic representation of the flow of wealth that goes in the opposite direction.  Electric current is the flow of positive charge, while electrons are negative, so the actual “flow” of charged particles is usually in the opposite direction of the current.  In just the same way, money flows in the opposite direction of wealth.

Of course, if you sell all of your assets, you no longer have them - you have the money instead.  This money symbolises the amount of wealth you have released from your control, and gives you the right to purchase other wealth from the wider economy.  That could be food, other inventory, a different factory, or shares in a company.

There is an important distinction here though - what would happen if you sold your assets, then put all of that money into a pile and set fire to it?  Aside from this being illegal in many countries (though surprisingly not in the UK), you wouldn’t have consumed anything - the assets you sold would still exist.  The only thing you would have done would be to exert a slight deflationary pressure on the currency - everyone else possessing units of that currency would be able to buy very slightly more with their money.  It would have the same effect as if you had taken all of the money and transferred a bit of it to everyone else in the world in proportion to how much of that currency they possessed at the time.

On the other hand, what would happen if you had destroyed your assets?  Well, obviously, they would no longer exist.  This would be a shame - someone else could have used them, and now if anyone wants them they will have to be made again, using someone’s time that could have been used producing something else.  The idea that destroying things helps the economy as you can pay someone to recreate them is a classic example of the “broken window fallacy”.

II. Creating and Destroying

Viewing wealth in this way is very helpful to make sense of a few things.  Whilst money circulates in the economy in the opposite direction to the movement of wealth, it is only useful when it is being transferred around.  You could almost take the view that money that is sat still ceases to exist - just as setting fire to a pile of cash “reduces the supply of money”, making the remaining money worth slightly more, even just stuffing it into your mattress would have a similar (albeit more temporary) effect.  If cash is taken “out of circulation”, the supply of money in the economy is reduced.

If you put your money into a bank account, there is a slightly different effect.  There is a common misconception that cash deposits in banks generate additional lending - that the additional cash allows banks to lend more money out.  It is true that there is a direct relationship between the two, but it is actually the opposite way around - additional lending creates more cash.  Don’t take my word for this though - the Bank of England has a great summary of how fiat currency works.

In much the same way that banks "create money" by advancing loans, repaying a loan “destroys money”. Just like matter annihilating with antimatter, it cancels out the debt that the bank holds (though thankfully, without the exciting explosion).  As before though, this is not a problem, as destroying money isn't the same as destroying wealth.

Even if you aren't directly repaying a loan, just depositing your money into a bank account has a knock-on effect that results in the bank seeking to acquire more debt to offset your deposit. Your deposit could be viewed as reducing the money supply, but unlike stuffing cash under your mattress, it also simultaneously increases the bank's demand for debt, which is equivalent to a decrease in the demand for money (debt is just negative money after all).

This means that unlike stuffing it under your mattress, putting money in the bank is not deflationary. (N.B. This is one way of describing this process - there are several others. Much like quantum mechanics, there are many different "interpretations", but they all result in the same calculations and the same outcomes. I am also glossing over several details, so I recommend reading the BoE paper linked above.)

This also partly helps to explain “Quantitative Easing” - the government “printing money” also doesn’t create wealth - it just increases the amount of cash floating around that can be used to purchase things.  By increasing the amount of cash without a corresponding increase in the amount of debt, it increases the money supply and therefore exerts an inflationary pressure, which has the effect of reducing the value of any cash that people have sat in bank accounts (or mattresses).

This can have a very powerful effect - the economy isn’t static, so whilst the amount of wealth is important, the flow of money also does have a critical role to play. (N.B. This is a slightly different mechanism to the monetary policy of changing interest rates to influence inflation. Low interest rates increase the demand for loans, and decrease the demand for cash. It is this decrease in demand for cash that exerts an inflationary pressure, rather than an increase in supply.)

Many businesses rely on a steady influx of cash, and cannot survive for long if this is disrupted (as we have seen during the recent pandemic related economic crisis).  This is usually due to staffing costs and loans - layoffs are unpopular and re-recruitment is costly, whilst loans cannot be avoided without declaring bankruptcy or liquidating assets to repay them. Therefore if the flow of money around the economy slows down companies with high leverage or many staff will be the first to downsize or fail.  Again though, QE is a policy that simply aims to increase the speed at which money changes hands - it doesn’t create wealth out of nothing, as using these definitions money is not wealth.

III. Explaining Stagflation

One example of a counterintuitive economic concept that becomes very clear when viewed from this perspective is stagflation - inflation that occurs despite slow growth and high unemployment. This is something that was considered physically impossible by economists, right up until it happened in the 1970s.

If you look at the supply of money relative to the amount of wealth, inflation occurs when the ratio of money to wealth increases, whilst deflation occurs when this ratio decreases. These can however both happen in two different ways.

If you print money, this generally increases the money supply more rapidly than the speed at which the amount of wealth is increasing. This is the canonical way in which inflation is framed - it will make each unit of money able to buy less wealth. Burning money will clearly have the opposite effect: decreasing the money supply and therefore making each unit of money able to buy more wealth - deflation. If however, rather than changing the supply of money, we adjust the other side of this equation, we get some interesting results.

In particular situations such as a tech boom, wealth is able to increase very rapidly. This can outpace the central bank's planned increases to the money supply, which causes deflation. Products become cheaper (or money becomes worth more, depending on your perspective), but unlike the standard view of deflation as a sign that an economy is struggling, this is a direct result of economic success.

Equally, if we are in a situation in which wealth is decreasing, this is inherently inflationary - there is less wealth to buy with the same amount of money, so the wealth costs more (or the money is worth less). The go-to example of this happening is the oil crisis in the 1970s - suddenly oil was much less available than before, despite its usefulness to the economy being unchanged. This limitation was a dramatic reduction in the amount of wealth present in the economy, and it impacted many sectors simultaneously, from transport to manufacturing, further reducing wealth by reducing productive capacity. There was much less available to be bought, but there was the same amount of money to buy it with, so the money became worth less.

Further to this, the demand for each can be changed too. As mentioned previously, changing interest rates does this from a monetary perspective. Adjusting the appeal of holding cash versus owning assets or equities changes the demand for cash. Interest rate reductions decrease demand for cash which is inflationary, while interest rate increases have the opposite effect.

Changing the demand for wealth is a little more subtle - it requires some sort of cultural factor. As an extreme example, during the dot-com boom, the amazing stock market returns were heavily publicised, making many people that wouldn't have ordinarily been investors want to get a piece of the action. This was a cultural shift that increased the demand for wealth. More generically, a bull market is a less extreme example of a sustained increase in demand for wealth.

A bear market is the opposite of a bull market, in which low demand results in falling prices. If anti-consumption caught on as a trend, without a corresponding increase in investment, this would similarly reduce the demand for wealth, driving prices lower. These can be collated together into a table as follows:

The important thing here is that whilst inflation and deflation themselves obviously have a very real impact on the economy, the last column comes with other effects. In fact, the inflation/deflation is really a side effect of what is occurring to change the amount of wealth present.

IV. Consumption is Not a Good Thing

Consumption is often described in a positive way as something that “drives growth” in our economy.  What actually is consumption though, looked at from this perspective?

Consumption is simply the destruction of wealth.  This sounds obviously bad, but in reality some of it is unavoidable.  Eating food is consumption - you are taking food (something that has value) and turning it into waste (something that has negligible value).  People have to eat to survive though.  You could say that without being eaten, food would spoil anyway, so it isn’t really “destruction of wealth” - the wealth was transient.  That however makes the assumption that the food was going to be produced regardless.  Food is only grown because it is expected to be in demand.  Once something with a limited shelf life is produced, it will inevitably be consumed (either by someone, or by being wasted), and so would be best consumed in a way that helps someone survive, or generates some happiness for someone rather than being wasted.  If nobody wanted the item however, the time and resources used to make it could have been spent elsewhere.

Consuming for survival is therefore difficult to argue against, but in the modern world, survival comes at a relatively small cost.  (The fact that some people are unable to afford even this small cost is a failing of our society, but is something I have written about before, so will not dwell on here).  The consumption that would be sufficient for everyone to survive would be a tiny fraction of our current consumption.

Using a factory to produce goods is also consumption in its own way - the factory will need more maintenance if it is in use.  It gets maintained, because it is producing more wealth that it is consuming.  This consumption is therefore also difficult to argue against - whilst wealth is consumed, more wealth is produced, so this is a net positive contribution.

Aside from consuming to survive and consuming to produce more, there is also consuming for enjoyment, or to increase your happiness.  At this point it is important for me to note that I am not against enjoyment - life is there to be enjoyed, so I am not making any sort of absolutist argument that “doing anything other than producing or consuming to survive is bad”.  We should absolutely enjoy our lives, and some amount of consumption is a reasonable price to pay for this, but we mustn’t lose sight of the reality: that consumption (by which I mean destruction of wealth) makes us poorer as a society.

Going for a walk in a forest and eating a spoonful of caviar are both activities that people engage in to gain enjoyment.  Going for a walk consumes very little - you may have to eat slightly more, and it will slightly reduce the longevity of your shoes, but the wealth destruction here can be measured in pence.  On the other hand, eating caviar is extremely expensive - you are taking something you have paid hundreds of pounds/dollars for and effectively flushing it down the toilet.  Obviously people gain some enjoyment from the process, but the cost of that enjoyment is enormously higher.

Again - initially people not eating caviar would result in a large waste in caviar, or caviar prices reducing dramatically.  This waste or drop in prices would however make caviar production less profitable, encouraging the people working in the industry, and the assets deployed in the caviar’s production to be put to other use.  The expense of the caviar is indicative of the time, effort and resources deployed in creating it, which therefore indicates the amount of wealth that could otherwise have been produced had this time, effort and resource been utilised differently.

Effectively, consumption is just one big broken window fallacy - for everything that is consumed, something needs to be produced to replace it, and that effort could have been otherwise utilised had the consumption not occurred.  Whilst our economy is heavily reliant upon consumption, making Keynesian policies such as stimulus undeniably necessary and effective to avoid turmoil when there is a drop in consumption, this does not change the underlying reality that any consumption ultimately reduces the amount of wealth.

This is very much reminiscent of the idea that work is an objective in itself.  The philosophy that job creation is the aim of a healthy economy is completely backwards.  Productivity is the thing that is desirable, whilst work is just a necessary evil to achieve productivity.

Work sucks, that’s why it isn’t called “fun”.

Bruce Bethke

Productivity cannot be achieved without work, but work is not the aim - if the same productivity could be achieved without work, that would be preferable.  In fact, the poet Wendell Berry expressed it very well:

People talk about “job creation,” as if that had ever been the aim of the industrial economy. The aim was to replace people with machines.

Wendell Berry

The thing is though - I get the feeling he thinks this is a bad thing!  Accomplishing more whilst working less is great, and industry has enabled this to happen.  It is in exactly this way that we should view consumption - it is not the objective.  Happiness (and at the very least, survival) is the thing that is desirable, whilst consumption is just a necessary evil to achieve happiness.  If we can achieve the same happiness with less consumption, that is a good thing.

These two ideas are inextricably linked, because productivity is what provides us with the consumables we need to survive and to improve our happiness.  The more we consume, the more work we have to do, in order to replenish the consumed items.  Just as more efficient production results in less need for work, if we can attain happiness with less consumption, that will result in less need for work too.  The less we work, the more time we have to spend cultivating our own happiness, so achieving the same level of happiness with less consumption should actually improve levels of happiness in our society even further.

V. Investment vs. Consumption

The alternative to consumption is investment - if you work hard, and save your money, you have contributed wealth to the world, and have not consumed it.  In principle, the money you have saved is representative of the difference between the wealth you have “released into the wider economy” and the wealth you have acquired for your own personal use.

If you spend money to acquire wealth, you don’t necessarily have to consume it.  You can instead accumulate assets that will persist until they degrade or are destroyed (both of which are consumption).  If you use these assets to produce more, you will be contributing further wealth to the world, and will therefore generate more money.  If instead, you consume them, they will be gone, and all of the effort that was put into making them will be gone too.

Fundamentally, any wealth you have acquired for your own personal use can either be consumed or maintained, and maintaining wealth is investment.  This is the essence of capitalism - using capital (the wealth you control) to generate further wealth.  Further distilled, you could view capitalism as the idea that investment is good, and should be rewarded.  Holding money in a bank account isn’t quite the same as investment, but it is at least the absence of consumption.  As we have established - some consumption is unavoidable, but if we accept the view that investment is good, then consumption cannot be desirable.  After all, if investment is the creation and preservation of wealth, then consumption, as the destruction of wealth, is its opposite.

As a more abstract but ultimately easier to manage model for investment, we can consider investment in companies.  Initially, let’s just consider companies issuing shares, as other transactions have more complicated mechanics.  By buying shares issued by a company, you are providing them with the means to acquire further assets/employees to improve their productive capacity, and in exchange, you get to own part of this productive capacity.  This is very similar to just accumulating assets yourself, but it is an abstraction layer - you don’t need to know which piece of machinery is yours, you just jointly own all of the company’s assets with all of the other shareholders.

This helps us to understand the wealth of billionaires.  Bill Gates and Jeff Bezos don’t have literal billions of dollars in their bank accounts.  They own a lot of shares in some very large and successful companies - this is indeed wealth rather than money.  It is the easy valuation of listed companies that allows us to confuse the two, and interpret as “money” the billions of dollars worth of assets that they control.

The idea that they could “feed the world” with this wealth is a bit disingenuous.  They could of course just sell the shares they own, and use it to buy food, but what is the end result of this course of action?  Buying such a large amount of food, and the transport to get it to where it needs to be would be quite disruptive, and would likely drive up the costs of both food and transport, meaning that a naive calculation of “what it would cost to end world hunger” using current market prices is likely to be quite an underestimate.

Let’s ignore this glaring issue though, and plough on regardless - what does it mean, to sell a large quantity of assets in order to spend billions of dollars buying food?  Whilst it is highly improbable that this financial transaction will result in the entirety of Amazon’s assets being liquidated and somehow converted into food, that is equivalent to what is occurring in wealth terms.  You are going to acquire billions of dollars worth of assets, and then consume them.

Please note - I am not saying here that we shouldn’t try to feed the world, or that it would be a waste to try to save peoples lives.  I am simply trying to frame the conversation in a more accurate way.  It is highly misguided to make statements like “Jeff Bezos is just a greedy person, sitting on all that money when he could be saving lives”.  Instead, we have to acknowledge that for us to achieve this humanitarian miracle, we would have to take wealth equivalent to a company the size of Amazon, with all of its productive capacity and therefore its ability to make life easier for millions of people, and we would have to consume it.  The fact that it wouldn’t be Amazon itself that ceased to exist is irrelevant - an equivalent amount of wealth would have been consumed.

Jeff Bezos is just the custodian of this wealth.  It can and should be argued whether one person should be the custodian of such a comparatively large amount of wealth.  Indeed, the control that multibillionaires have over the economy, labour practices and even the government is something that should concern everybody.  This is however a very different way of framing the problems with over-concentration of wealth than the self-righteous polemics against the greed of the wealthy that seem to be published regularly.

Breaking up large companies to curb monopolistic tendencies, and having strong labour and anti-lobbying regulations are very different proposals from “take wealthy people’s money and spend it”.  The government does invest a lot of money in infrastructure and education, but it does consume a lot too.  Few governments have the self-control to curtail their consumption sufficiently that they are able to sustain a sovereign wealth fund.

VI. Loss of Control

The amount of money that changes hands can be greater than the amount of wealth that you consume - if you hire a fancy limousine, or buy a luxury watch from a company, you can reasonably expect a significant portion of what you spend to go straight to its profit margin. Of course, the goods/services being more expensive might partially be due to a greater amount of wealth being used to provide them - the watch might be better made and longer lasting, which would take more effort, and the limousine might use more fuel than a normal car and be more expensive to maintain.  Despite this though, high end brands are usually able to command a premium above and beyond that which their wares would fetch in the absence of the brand.

Any money that contributes to a company's profit margin isn't representative of wealth being directly consumed. After all, the profit margin is exactly the difference between the effort and expense required to make/do something and the amount you actually paid for it. Instead, this portion of the money is a transfer of the right to control that amount of wealth.

The recipients of this money can then spend it as they see fit; using it to acquire wealth, which could be invested or consumed. A company might choose to invest it in order to expand or consume it by throwing a party for their employees. A third option would be to pay a bonus to their CEO or pay a dividend to their shareholders - this would again pass on the right to control the wealth. The shareholders might choose to invest their windfall, or they might choose to consume it instead.

Once you no longer possess the money however, you do not control it, therefore you cannot determine what it is used for - whether the wealth it is used to acquire gets consumed or not. In the same way, once you have sold assets, you don’t control them anymore, and you can’t stop someone from consuming them. Just because you have cash in the bank, doesn't mean that the wealth that cash represents can't be destroyed. The wealth you sold is not directly tied to the cash, so the cash won't become worthless if the wealth is consumed; instead as mentioned, this loss of wealth is distributed across all cash as inflation.

How do you stop wealth you control from being consumed, without having to manage a load of assets yourself? Well, thankfully in the modern day this is really very easy - you buy shares. Rather than having to maintain a bunch of assets, and having to work out how to use them most productively, owning shares in companies means that you are effectively employing the company's executives to do this for you. Companies are set up to maximise shareholder profit, which means that their goal is to use the wealth they control to generate as much additional wealth as they can.

As with most things, this can break down if taken to the extreme. Companies can generate negative externalities that their profitability does not capture, such as environmental damage, employee exploitation or monpolistic tendencies. From a personal finance perspective, you should also have a well diversified portfolio, so that you are not over-exposed to any particular asset class or location. In general though, this "maximise shareholder profit" maxim is exactly what you want, if you intend to use your wealth to generate more wealth, rather than risk it being consumed.

VII. Capitalism isn’t Consumerism

In my last post, I talked about capitalism, and how it is often conflated with a number of societal ills, including consumerism.  As above - the accumulation of wealth in order to use it to create further wealth is the core tenet of capitalism, making consumerism fundamentally anti-capitalist.  How then do we end up with consumerism in a capitalist society?

This is an important question, as it is demonstrably the case that our society is quite consumerist, despite ostensibly being based on capitalist principles. We can look no further than Adam Smith himself - the "father of capitalism" for an insight into why this is:

Consumption is the sole end and purpose of all production; and the interest of the producer ought to be attended to, only so far as it may be necessary for promoting that of the consumer.

Adam Smith - The Wealth Of Nations

As this article argues, Adam Smith didn't foresee the full extent of the industrial revolution, however in a certain context, he is not wrong. Ultimately, most of what we do is aimed at increasing our happiness in some way.  It is just a question of whether we are consuming (in order to satisfy ourselves right now), or investing (in order to be able to satisfy ourselves more or more cheaply in the future).

Investment in productive capacity can enable us to produce things more efficiently, allowing us to satisfy ourselves the same amount, but consuming less wealth while doing so.  Investment in the arts can give us more art to enjoy, allowing us to satisfy ourselves more.  It would be unhelpful to suggest that we not consume anything beyond what is necessary to survive and increase our production, as this flies in the face of everyone’s ultimate goal of living a happy contented life.  That said, if we understand the trade-off between consuming now versus investing for the future, it can help us to improve our happiness and our society in the long term.

I will argue that there are two forces pushing a capitalist system towards consumerism, and that these forces do make consumerism a natural consequence of capitalism when taken to its extreme.  However, rather than rejecting capitalism entirely as a way to stem the tide of consumerism, this tells us instead where we need to regulate and rein in capitalism.

VIII. Status Symbols

The first force is the social pressure on people to appear “high status”.  Different societies and cultures have different measures of status - in Tang Dynasty China, being accepted into the civil service was a sign of success in life, and such positions were highly sought after, whilst in the Roman Republic, victorious military leaders were the most lauded citizens.  In the middle of the 20th century, professorship was one of the most respectable careers, with academic success being prized even if it wasn’t particularly lucrative.

In our modern society, there are a couple of key sources of status - fame and wealth.  The former often begets the latter (c.f. Film stars being able to command large fees), whilst the latter is increasingly resulting in a kind of fame (with Bill Gates, Jeff Bezos, Elon Musk and Mark Zuckerberg becoming household names).

Status games are inevitable - some people may be immune to the desire for high status, but most are not.  Capitalism makes a value judgement that wealthy people have done something good - produced more and consumed less, which means that individuals with high wealth are natural role models within a capitalist society.  This is not in itself necessarily a problem, but the problem arises when people care more about appearance than substance.  Wealthy people are able to consume a lot more than others, so if they care about whether or not they appear wealthy, they might choose to consume more than they otherwise would.

The aforementioned caviar is of course a good example of this.  At £20,000 per kilogram, Beluga caviar isn’t a thousand times more delicious than steak - it allows people to demonstrate their social status through conspicuous consumption.  Luxury yachts are not quite consumption in themselves - they are an asset that could be put to productive use, but they are usually not.  This makes their purpose fundamentally one of conspicuous consumption - they take money to maintain, and even more money to staff and to use.  All of this consumes wealth, and it isn’t done to enable the yacht to create more wealth.

Conspicuous consumerism doesn’t just apply to the wealthy people that can do so without difficulty - in an attempt to appear “high status” many people that could live a perfectly comfortable life end up in debt as they try to “keep up with the Joneses”, consuming more than they need in order to signal a greater wealth than they actually have.

This is not to say that all of these "high status" actions are terrible. For example, getting a taxi isn't always an unnecessary expense. If you drove yourself, you would have been consuming your own time and effort. This means that if your time is particularly valuable and productive, perhaps using a driver would be a net positive, which is why most CEOs have chauffeurs.

All this being said, conspicuous consumption is not a problem that is unique to capitalism - it has been observed in one guise or another for as long as we have recorded history.  For this reason, it is not easily resolved, and capitalism shouldn’t take all of the blame, but valuing the accumulation of wealth may well exacerbate the issue.  Some cultures have developed a stigma attached to conspicuous consumerism, viewing it as “tacky”, which may serve as a useful opposing force, though cultivating this aspect of a culture is likely to be quite a difficult endeavour.

IX. Advertising

The other key force that leads capitalism down the path towards consumerism is advertising.  Advertisements can simply inform people that a product exists - arguably a useful service.  This is however not usually the limit of the advertiser’s power, as over time we have become more sophisticated at manipulating people, and even our culture itself through the medium of advertising (c.f. Women’s shaving products).  Companies are now adept at inventing insecurities for people to worry about and spend money on - they can tell people what they want, and therefore artificially increase demand for consumption.

Much of this advertising plays on encouraging the kind of status games discussed in the previous section, but even aside from that, there is a lot of money to be made in convincing people to be unsatisfied by things that previously made them happy.  A company can’t make much money from you if you are content with what you have, so it is in their interest to make you feel like you are missing out.

Rather than living happy contented lives, taking leisurely strolls in nature, comfortable in the knowledge that food is readily available and cheap, we instead persist in the rat-race of 9-to-5 jobs earning money so that we can consume more.  The latest iPhone, a new widescreen TV, caviar, you name it - all reduced to rubbish and discarded when the next one comes out, having given us fleeting enjoyment and leaving us with no more wealth than we started with.  The people producing these consumables have found an exploit in the system - they are capitalists, but they have used advertising to convince other people to be non-capitalist.

There are many people living paycheck to paycheck - 41% of the UK don’t have enough in savings to live for a month without income.  To be very clear - there are many of these people that have no choice - they have very low incomes, and so are just consuming to survive.  After the state pension, the largest DWP program is Housing Benefit with 3.8 million claimants.  All of these people, whether pensioners, unemployed or working poor must have very little income, so it is no surprise that they are unable to make savings (also, given the way benefits are administered, if they saved too much, they would become ineligible for benefits).  In its mission to reduce poverty, the Joseph Rowntree Foundation also collects data on the working poor, and they calculate that there were around 4 million people that counted as working poor in 2019.  There will be significant overlap between people on Housing Benefit and the JRF’s working poor figure, but if we make the (for these purposes) very conservative assumption that there isn’t any overlap, that would mean there were 7.8 million people in the UK that are completely unable to make savings.

This is still less than 15% of the adult population of the UK though, so what about the other 26% of people that are not living in poverty, but still live paycheck to paycheck? These people are earning money, and spending it immediately on items they consume.  Unlike the poorest citizens, who are consuming in order to survive, and need government assistance to be able to manage that, these people are consuming because they want to.  They remain unable to afford to invest - paying their money to the capitalists, rather than being capitalists themselves.  They are the archetypal consumers.

X. The Incentive to Encourage Consumption

After all, if you buy something from a company, they get to keep whatever profit margin they are making - they have no further obligation to you.  If you invested that money into the company instead, it would have to pay you a share of the dividends - effectively diluting the current owners.

Wait, I hear you say - this only happens when companies are issuing new shares!  Buying shares on the stock market doesn’t usually dilute anyone or create new obligations, it just increases their share price.

Well - assuming that a company isn’t issuing shares, and that you’re just buying them on the open market, it is true that investing in a company doesn’t dilute anyone’s shareholding (unless they happen to choose to sell shares at the same time).  What it does do however, is slightly increase the demand for shares.  This can be looked at in a couple of ways:

1. The person you bought the shares off now has money they have to do something with, and assuming they want to invest it, they need to find something to invest it in.  They invest it in another company, setting off a cascade of buyers and sellers until at some point in the chain, someone invests in a share issue, a bond or some other form of investment that directly adds money to the system, allowing a company to acquire some equipment/employees.

2. Alternatively, you can look at it another way - although share prices in a liquid market are very elastic, it is still the case that buying shares will shift the share price a small amount.  If demand goes up enough, it will increase the price of shares, which will decrease their yield.  This lower yield makes other riskier shares more attractive, again causing a cascade effect in which an investment in a blue-chip company can marginally increase the demand for new shares in a start-up.

Both of these perspectives give you a result that is less desirable for the company’s owners than just making a small profit out of your consumption.  This brings us back to advertising - if you can encourage people to consume rather than invest, you get more money with no strings attached.  Promoting consumerist attitudes is profitable for a great many companies, so they advertise aggressively to make people want more stuff.  

XI. Conclusion

So - consumption is not desirable. Whilst consumption is unavoidable, and it is in a limited sense the end goal of production, the excessive or conspicuous consumption that is consumerism is in fact anti-capitalist.  Despite this, I have argued that consumerism occurs when capitalism is allowed to progress unregulated.  When companies are allowed too much scope to influence people and culture through advertising, consumerism becomes inevitable.

To combat this, strong advertising regulations are critical - the UK’s advertising standards agency generally does a good job of this, ensuring that adverts are factual and not misleading.  Adverts in the US don’t appear to have any such limitations, which leads to claims like “Pop-tarts - a good source of vitamins” - these statements rather amusingly have to be covered up before such products can be sold in the UK.

Personally though, I don’t think the UK goes far enough - adverts are still able to make people unhappy with their current situation, pushing “aspirational” lifestyles that stoke people’s envy.  We have done something like this with alcohol advertising, for which there are very stringent rules about not making drinking look “cool” to young people and not encouraging excessive drinking.

Of course, to have strong regulations around advertising, companies need to be prevented from becoming too large and powerful.  Once a company is large enough, it either becomes too important to a country’s economy for politicians to be able to risk disagreeing with its board (c.f. Samsung’s influence in South Korea), or it simply becomes able to buy (oh, sorry - I meant “lobby”) politicians.

This means that in a healthy capitalist society, companies need to be prevented from becoming too large or powerful, otherwise they may start engaging in these harmful behaviours.  Again, the UK has this to some extent in the Competition and Markets Authority (CMA), whose main brief is to police monopolistic behaviours that might harm the interests of “consumers”.  This specific focus on consumers does however seem to often miss the impacts of mergers on the wider economy (suppliers, competitors, supporting industries, etc.), which are important to consider when trying to avoid excessive concentration of power.  The CMA’s decision to block a merger between Sainsbury’s and Asda in 2019 was unexpected given previous precedent, but I am inclined to see this change in approach as long overdue - together they would have made up over 30% of the UK’s grocery market.

Concerns about concentration of power are also relevant for individuals, so it is important to consider ways in which we can limit the power of wealthy people in a capitalist society.  Further to this, as mentioned at the start of this post, anything that might subvert the link between the amount of wealth someone produces and the money they receive for it needs to be carefully monitored and minimised.  Worker exploitation and poorly negotiated contracts are obvious things that are often regulated by governments, but taxes also need to be carefully managed to not disrupt growth by introducing perverse incentives.

Controls and regulations that would be beneficial to a capitalist society:

• Limits to advertising - ensuring adverts are factual, not misleading and are not trying to make people unhappy with their current situation.

• More restrictions around mergers between large companies, and a greater willingness to break up large companies that hold too much market share.

• Strong restrictions around lobbying, bribery and the “revolving door between government and business”.  Better pay for politicians and government officials (as is done in Singapore) might help this.

• Reducing the barriers to small investors, to encourage all people to partake in the ownership of companies.

• Strong penalties for business practices that involve large businesses bankrupting small companies in order to buy them or their intellectual property at bargain prices.

Does this mean we should give tax cuts to the rich, rather than paying welfare to the poor?  No! Survival is important - it shouldn’t need to be said that people dying is bad.  Developed countries are now at the point where survival driven consumption is tiny in proportion to the sizes of their economies.  With the increasing likelihood of AI being developed in the next few years, we need to be sure that the bounties of a successful economy are of benefit to all people.  Arguments that suggest that allowing people to die might be economically beneficial have lost sight of what the goal of humanity should be.  We want an economy that makes life good and happy for people - if the economy would be more efficient if humans were wiped out, so that production could be higher and consumption lower, that is missing the point completely.

Does this mean that we should stop worrying about wealth inequality?  No!  Control of wealth is important, and if too few people control too much wealth there are all sorts of problems that arise. Concentrated wealth is like putting all of your eggs in one basket - what if someone who has consistently made good investment decisions suddenly stops being competent? If any individual is in a position where a mis-step by them could crash the economy, that is a huge risk.  Concentrated wealth is also a risk to democracy, as anyone with an amount of wealth comparable to a small country has the power to apply significant leverage to politicians (even in a big country) to get what they want.  Too few people making investment decisions in an economy reduces the diversity of ideas - the beauty and efficiency of markets is due to the effect that a large enough number of people’s estimates for the value of an item converges on the item’s actual value. By reducing the number of people actually participating in the market, you lose a huge amount of information.

Hopefully this explains why I think that capitalism has the potential to be a good thing in its own right.  Also, it might explain why I find the suggestion by the UK’s Chancellor of the Exchequer Rishi Sunak, that people help the UK’s economy by spending all the money they have saved up over the last 9 months, quite so infuriating.

The huge improvement in people’s standard of living over the last hundred years has been one of the biggest successes of Capitalism.  The ability of capitalists to offer loans allowed entrepreneurs to generate improved growth and employment.  With money from investors, companies have been able to achieve enormous technological advances, resulting in leaps in quality of life for many people.  The improved efficiencies of competitive industry have lowered prices of many goods, lifting millions out of poverty. 

The main thing standing in the way of even greater improvements in people’s happiness and standard of living, is that the markets are still not yet free enough.  Government is stifling the markets with regulation that raises the costs of doing business and discourages investment.  State benefits discourage workers from finding more enriching jobs, instead encouraging reliance and stagnation.

Despite the US’s historic progress in the direction of free markets, true libertarianism, in which the government is small enough to completely free the market from interference has never truly been attempted.  All of the economic and societal failings of the US can be traced back to the government interfering with the free market – whenever a problem arose, the US government attempted to introduce legislation to resolve it, rather than allowing the market to resolve it naturally. This exacerbates the problem rather than resolving it, so we should instead strive to further reduce the size of government, until true free-market libertarianism can be achieved.

Second – an alternative, equally extreme view:

The huge improvement in people’s standard of living over the last hundred years has been one of the biggest successes of Socialism.  The ability of labour to form unions allowed workers to negotiate improved wages and working conditions.  With revenue from taxes, governments have been able to achieve enormous technological advances, resulting in leaps in quality of life for many people.  The social security programs of compassionate governments have raised incomes of the poorest, lifting millions out of poverty. 

The main thing standing in the way of even greater improvements in people’s happiness and standard of living, is that the government is still not yet powerful enough.  Companies are manipulating the government with lobbying that reduces the spending on social programs and cuts taxes.  Stock markets discourage companies from paying workers a fair wage, instead encouraging exploitation and inequality.

Despite the USSR’s historic progress in the direction of social welfare, true communism, in which the workers control the capital enough to completely free the populace from servitude has never truly been attempted.  All of the economic and societal failings of the USSR can be traced back to powerful individuals interfering with the will of the people – whenever a problem arose, the USSR government attempted to divert attention away from it, rather than allowing the workers to resolve it naturally. This exacerbates the problem rather than resolving it, so we should instead strive to further increase the workers’ control of capital, until true democratic communism can be achieved.

You hopefully see what I did there.  I have written the same passage, about the same thing, changing as few words as I can: 

The huge improvement in people’s standard of living over the last hundred years has been one of the biggest successes of ___.  The ability of ___ to ___ ___ allowed ___ to ___ improved ___ and ___.  With ___ from ___, ___ have been able to achieve enormous technological advances, resulting in leaps in quality of life for many people.  The ___ ___ of ___ ___ have ___ ___ of ___ ___, lifting millions out of poverty. 

The main thing standing in the way of even greater improvements in people’s happiness and standard of living, is that the ___ ___ still not yet ___ enough.  ___ ___ ___ the ___ with ___ that ___ the ___ ___ ___ and ___ ___.  ___ ___ discourage ___ from ___ ___ ___, instead encouraging ___ and ___.

Despite the ___'s historic progress in the direction of ___ ___, true ___, in which the ___ ___ ___ enough to completely free the ___ from ___ has never truly been attempted.  All of the economic and societal failings of the ___ can be traced back to ___ ___ interfering with the ___ ___ – whenever a problem arose, the ___ government attempted to ___ ___ ___ it, rather than allowing the ___ to resolve it naturally. This exacerbates the problem rather than resolving it, so we should instead strive to further ___ the ___ ___ ___, until true ___ ___ can be achieved. 

Both give plausible explanations of why the positive outcomes we see are a consequence of adherence to their particular pet theory, and both explain away the counterexamples as simply being a result of inadequately strict adherence.  A lot of what both views say sounds plausible, but successive paragraphs make much stronger and more questionable claims.

The first paragraph of each is quite reasonable – I can happily agree with both of them, and they do not contradict each other.  Both capitalism and socialism have in part been hugely beneficial to the modern world, in very different (and quite likely complimentary) ways.

The second and third paragraphs of each however go too far – there are elements of truth (some regulations can be bad, Stalin hijacked the communist agenda), but they claim too much, accepting none of the responsibility for failures, and instead advocating for “too much of a good thing”.

The second and third paragraphs of each are both examples of “Hedgehog thinking” - there is one overarching idea, and all data must support it, because it is the correct idea.  Seemingly contradictory data is actually supporting data; you just need the right way to phrase it.  Fox thinking, on the contrary, is that there could be multiple things going on at once - reality is complex, and a theory that explains many things well can still have blind spots.

I am not claiming here that capitalism or free markets are fundamentally bad - far from it, however I often encounter arguments that they are fundamentally good and infallible.  Capitalism (just like Socialism) is a useful tool for humanity’s development, but it has blind spots, and may not produce the optimal outcome in all cases.

More than this though - I think these kind of views demonstrate the ease with which socialism gets conflated with repressive command-economy communism, and capitalism gets conflated with laissez-faire free-market libertarianism. I roll my eyes every time I hear someone on an American news network using the word socialist to imply that some sort of Stalinist purge is imminent. Equally though, I find myself almost as frustrated when I hear protesters denouncing capitalism in its entirety, when their issue is with consumerism/rentier landlords/monopolistic practices.

To claim that capitalism is synonymous with consumerism, destroying the environment, big business monopolies and shafting the poor is just as dogmatic and unhelpful as claiming that socialism is synonymous with nationalised industry, gulags and food shortages.

Blindly taking either philosophy to the extremes demonstrated in the second and third paragraphs is likely to have some pretty serious negative consequences, but the trick is to not be blind to these things. Capitalism and socialism have both made enormous positive contributions to human wellbeing in the last century and a half, but both have led to some outcomes that have not been so great.

We shouldn't shy away from addressing the issues that arise - it is not anti-capitalist to criticize a business for polluting the environment, just as it is not anti-socialist to criticize a union for opposing the introduction of a new technology. If you can't criticize, you can't optimize.

[Edit: I have changed my thinking on this topic following some discussion and further thinking on the subject. I am leaving this post up, but have added a new section changing my conclusion.]

As well as the general public voting for politicians or directly for policies, voting is also used by politicians themselves to decide on issues and pass laws.

Rather than being a "once every few years" phenomenon, this voting is part of the day-to-day workings of government. The standard operating procedure for many politicians.

This means that whilst some sort of formal procedure is needed, even the previously mentioned voting systems of Approval Voting, Score Voting, Evaluative Voting and SPAV are still far to rigid to permit the kind of nuance that is necessary in navigating the complex issues of the day. Rather like using a sledgehammer to crack a nut, too simplistic an approach leads to a broken system. Legislators and governments tend to eventually find ways around a procedure if it is too restrictive, but these loopholes are accidental and therefore do not necessarily yield the best outcomes.

The trouble is, that even using the systems mentioned above, there is insufficient room for the full range of support and opposition to be expressed. Filibusters are a good example of this - they are a way for US politicians to demonstrate extreme opposition to a bill. This action usually comes at a cost, but if a politician feels sufficiently strongly about an issue, they can singlehandedly prevent the bill from passing.

This is obvously far from ideal, as if overused it can prevent anything from getting done. Aside from this however, it is problematic because the cost to the politician is often unclear. Depending on the issue and the views of the other politicians, it could have very little long term impact on the politician, or it could render them a pariah, making people unwilling to work with them.

Pork Barrel Politics is an example from the other end of the spectrum - if a politician doesn't care one way or another about an issue, their vote is effectively up for sale. Bills can therefore be passed by including within them provisions that sufficiently benefit individual politicians. The cost here is usually borne by the state, again making it a less than ideal situation.

If pork barrel arrangements are able to be banned, this still doesn't remove the problem, as tyranny of the majority often manifests itself in these kinds of situations, where a large number of people have a very mild preference that is in opposition to a minority's strong preference. Even using a method such as Score Voting, it costs politicians nothing to vote in line with their mild preference, and without any pork to benefit from there is no reason for them to reduce the power of their vote. This results in them outvoting the minority despite their virtual indifference.

Because voting on issues is a fundamental part of a politician's job, we can allow for a system of procedural voting that is significantly more complex and nuanced than what we could reasonably expect the electorate to deal with. The effort of understanding the nuances of a system is not really worthwhile if you are only using it once every couple of years, but if you are using it daily, the effort pays off. If we therefore allow ourselves to consider systems that have more complexity, what can we accomplish?

Some people may have read my previous 3 posts, and been wondering why I haven't mentioned Quadratic Voting yet. In a modern democracy, voting is open to almost everyone in society, so the systems used need to be accessible not just to the average person, but to the vast majority of people. Every additional complication that is added will lose a certain proportion of people, and this contributes to sentiments that a system might be undemocratic (another advantage that approval voting has over ranked methods). Perhaps in some halcyon future, the majority of people will have the time and energy to get comfortable with the nuances of Quadratic Voting, but for now I am not proposing it as a panacea. I am raising it only as a solution to the specific problem of procedural voting, in which the people involved have the resources and incentives to become adequately familiar with it.

Quadratic Voting

The two examples of system loopholes above have something in common - there is a price to be paid for not allowing a sufficient gamut of opinion.

One way to better capture this range of strengths of opinion could be to allow people to forgo their right to vote on one issue in exchange for being able to "vote twice" on another issue. This quite simplistic approach goes too far though - it now makes it too easy for highly motivated minorities to push through legislation. Rather than voting on other important items, politicians could be "free-riders", relying on other politicians to pass things while saving up their votes to ram through something unpopular.

On the one hand, this allows the system to internalise the costs associated with pork barrel politics, and reduces the need for things like filibusters to allow for strong opposition. The costs become something quantifiable that the politicians themselves bear. On the other hand, this reverses the tyrrany of the majority situation, putting too much power into the hands of highly motivated minority viewpoints. What we need is a system that internalises the costs, but allows for a better balance between minority and majority interests.

Quadratic Voting is a way of doing this that increases the cost of each subsequent vote on a particular issue. This still allows people a wider range of expression than in an ordinary "one person one vote" system, but means that it is not practical for a small minority to completely overwhelm a vote just by abstaining from other decisions.

How it Works

In a situation in which there are multiple issues to vote on, Quadratic Voting provides each voter with a "budget" which can be spent on votes. Voters can vote for, vote against or abstain on any particular issue. The first vote on any particular issue costs 1, as expected, however they can vote a second time on the same issue for an additional cost of 2. A third vote costs 3, and so on.

As a simple example, if there were 10 issues being voted on, and people had 10 votes, they could vote for (or against) each one of the 10 issues. If there were a couple of issues they weren't particularly invested in either way, they could instead abstain from two, and use those two unused votes to place a second vote on an issue that was particularly close to their heart. In any sensible implementation, it would be useful to distinguish between the numbers of votes themselves and the costs of the votes, so going forwards I will refer to voters as having a budget of "democracy tokens" which are used to "buy" votes. Of course, no actual money is involved, but the concept of "spending" the tokens is a useful one.

If only one of the 10 issues was one that a particular voter cared about, they could spend all 10 of their tokens buying votes for that particular issue. This would buy a total of 4 votes - 1 token for the first vote, 2 for the second, 3 for the third and 4 tokens for the fourth, for a total of 10 tokens. For those arithmetically inclined, you may notice that this means that buying n votes costs T_n tokens, where T_n is the n^th Triangular number. The formula for calculating this is:

which is where the "quadratic" in the name comes from (in fact this is functionally equivalent to a system where n votes costs n² tokens, but this is less natural to explain than "the n^th vote on the same issue costs n tokens").

The increasing cost associated with declaring a stronger preference allows some useful results from economics to be applied. As the number of votes on a particular issue increases, the cost per vote increases, meaning that the exact amount that a voter cares about an issue can be found (relative to the other issues being voted on in the same batch). At some point the votes on one issue will become so expensive, that even expressing a mild preference on another issue is so comparatively cheap that it is worthwhile.

Put simply, it allows voters to demonstrate the true value of what a vote on a particular issue is worth to them. A thorough explanation of the principles involved can be found on Vitalik Buterin's website, which I highly recommend if you are at all interested in the concept.

Implementation

The House of Commons usually has around 200 votes per year (give or take a dozen or so), which generally follow a debate, and can happen on any given day. Unfortunately, many votes don't have good attendance, often because they are issues that particular politicians are not sufficiently interested in to warrant attending the debate.

Rather than debating then voting, debates could be held during a month and attended by those that are interested, then votes could all occur on a single day at the end of the month - a "voting session" where all are likely to be in attendance. Obviously voting in advance of the session or voting in absentia would need to be permitted to avoid shenanigans (West Wing season 6 episode 17 is a fictional but excellent example of why this is would be necessary).

For every item to be voted on in the voting session, each representative/politician could be given 3 "democracy tokens". In an average month in the UK's House of Commons, there would be about 16 issues to vote on, so in this case everyone would receive 48 tokens.

As an aside, 3 tokens per issue is better than 1 which was used in the simple example above. This is because with only 1 token per issue, any additional votes on an issue necessitate that you forfeit an opinion entirely on other issues. With 3 tokens per issue, voters can still express a mild opinion on all votes, even if they want to express a stronger view on some.

Votes being taken in these monthly batches would mean that everyone knows what issues are available to be voted on. This would ensure that no-one spends all their tokens before being aware of an issue they care about more, or equally, save their tokens in anticipation of an issue, only for it not to arise. By extension, this means that people shouldn't be able to "carry over" tokens from one voting session to the next, as this could result in similar exploitable situations and behaviours.

It would also be important for voting sessions to not be on too few issues, as this would render the benefits of the system irrelevant and reduce it back to fairly ordinary voting. A session with too few issues being raised (perhaps fewer than 8) could be postponed and combined with the next voting session instead.

Within a legislative body, there are a small enough number of people that there is no requirement for voting to decide between individual options. The process of drafting a law could of course include some form of voting with multiple different options as a route towards finding the form of a law that is most likely to pass, but this is not an essential part of the process - such consensus building could rely on the use of sub-committees instead. The final binding votes however can be restricted to whether to pass or reject a specific measure, bill or law. This means that we don't need to worry about "spoilers" or any potential strategies that complicate votes with more than two options.

It would also be possible to define a threshold, like we did for referenda. Our current system effectively uses a threshold of 0 - a law can theoretically be passed with a majority of 1. To me, this feels too low - if the margin for success is so slim, it is better to stick with the status quo. A 10% threshold would avoid this eventuality but should avoid too much deadlock (allowing new laws to be passed only if they won 55%-45% or above). Perhaps though, a higher threshold would encourage more effort to be made in consensus building.

Either way, with the ability to vote multiple times on an issue, it would be possible for some popular initiatives to achieve support greater than "100%". This would mean that there were more votes cast for an initiative than there were politicians, but within this system that shouldn't be an issue. In fact, it would be fairly unlikely, as in a body of politicians if a large enough number support something, they would be aware of the level of support. Therefore, they would be unlikely to waste additional tokens paying for votes when it is almost certain to pass anyway.

Further Reading

As Quadratic Voting is a relatively new idea, it may be useful for me to include some resources giving more information about it. Below are a few links, starting with the original papers proposing the system:

• Glen Weyl & Steven Lalley's original paper on Quadratic Voting

• Glen Weyl, Vitalik Buterin & Zoë Hitzig's paper on Liberal Radicalism

• Glen Weyl & Eric Posner's book "Radical Markets"

• Eric Posner - Quadratic Voting

• Tyler Cowen - Thoughts on Quadratic Voting

• Eric Posner's response to Tyler Cowen

A few editorials on the idea:

• Vox Article

• Spectator Article - this article has been criticised as being misleading

• Hackernoon Article

A number of more technical blog posts about the topic:

• Quadratic Payments: A Primer (Vitalik Buterin's website as above)

• Quadratic Voting with Sortition (Highly relevant to my last post)

• Quadratic voting and types of one person, one vote

• Persistent Voting with Quadratic Voting

[Edit: Unfortunately, despite the ideas above being fairly well publicised, there have been criticisms that they are not quite as original or foolproof as might be being claimed. Firstly, this link section would not be complete without Warren Smith's analysis of monetised voting systems. This includes something of a polemic against Weyl and Posner's papers and claims.

Problems

Taking Warren Smith's comments into account, this system looks a lot less attractive, and opens up whole new cans of worms that must be reckoned with.

Monetised voting systems introduce the possibility that politicians could introduce "spam" bills. These would be easy to make threatening to a minority, forcing their opponents to waste tokens voting them down. This would then prevent the minority from being able to pass any of their desired legislation.

The lack of constraints on bills that could be introduced to a legislature makes the scope of this problem quite serious. There may be many other areas in which exploits could be found in this new, untested system.

Whilst it may be possible to find a use for monetised voting systems for very well constrained problems such as budget allocation, it is something of a solution in search of a problem. Indeed, if you're looking for a way to bring the power of markets to voting, Robin Hanson's Futarchy proposal is possibly a better place to start. At least betting markets are already an established and understood mechanism.

Per the previous posts, if some movement were successful in driving the introduction of Approval Voting for electing leaders, this would likely lead to less divisive politics and easier compromise. The further reform of selecting representatives using partitioned sortition would reduce their incentives to grandstand and obstruct. At this point, the issues raised above whilst not completely avoidable, are likely to be much less pathological, and more like occasional minor annoyances.

At this point, procedural voting would probably best be done using the same method as for referenda - Evaluative Voting with a sensible threshold. It is likely that a lower threshold than what is used for referenda would be helpful to avoid legislative paralysis, after all, there would be far more frequent procedural votes than there would be referenda. As can be seen from the situation in the US arising from the threat of a filibuster, forcing all legislation to require a supermajority before it can be passed is not a particularly efficient way of running a government.

Of course, different thresholds could be used depending on the subject matter of the vote - "constitutional" matters should require a higher bar of approval before the status quo can be changed. That said, ordinary votes should probably use a threshold of 2% to 10% of the total possible score. The easier it is for a government to pass something, the easier it is for a government to reverse it too.

Further to this, Evaluative Voting allows multiple versions of legislation to be considered simultaneously, removing the necessity for sub-committees, and facilitating consensus building. Of course, sub-committees may still have a place in drafting and in curating the alternatives, but being able to simultaneously vote on multiple versions of a bill could overcome a significant amount of deadlock.]

Conclusion

The right voting method needs to be used for the right purpose. In the first of these four posts, I identified 4 different situations in which voting is used, each of which has very different requirements. Having considered each in turn, the following methods currently look the most promising in each situation:

1. Leaders (Presidential/Gubernatorial Systems)

   • Approval Voting is a very simple method to use and to implement that avoids all of the most egregious pathologies that plague voting methods

   • Alternatively, Score Voting could be used if people were receptive to the slightly higher complexity

   • Either Approval or Score voting could be supplemented with a (non-automatic) top-two run-off vote, however a second vote adds expense, and turn-out in run-off elections tends to be lower than the initial vote

   • If a run-off was desired however, this would have to be as a separate election, as any kind of automatic run-off introduces pathological behaviour that negates many of the advantages that Approval and Score Voting provide

   • Even under a parliamentary system, a leader still needs to be elected by the parliament, and it would still be sensible for them to use Approval or Score Voting for this purpose

2. Referenda (Direct Democracy)

   • Evaluative Voting (Score Voting with the range {-1, 0, 1}) allows for the level of support for a range of possible motions to be accurately ascertained, allowing votes against to be qualitatively different to abstentions

   • A threshold between 10% and 50% of the total possible score would ensure that laws wouldn't change with a knife-edge majority

   • This system would remove the discontinuity caused by turn-out thresholds, removing the argument that people should abstain rather than vote against an issue they disagree with

3. Representatives (Representative Democracy/Parliamentary Systems)

   • Partitioned Sortition, whilst not strictly a voting method, allows for the selection of representatives in a way that virtually guarantees proportionality, as well as avoiding populism, misleading campaigns or relying on a political class

   • The partitions can be overlaid on top of one another without reducing "constituencies" to tiny groups that are too small to be represented, in fact the partitions can ensure that even fairly small groups of people are able to be appropriately represented

   • If sortition is not politically possible, then Sequential Proportional Approval Voting is a good method to generate a proportional body of representatives

4. Procedures (Intra-governmental decision making)

   • Quadratic voting allows a greater range of opinion to be expressed, when people are going to be voting on a large number of things in a similar timeframe

   • It internalises some costs that have previously been borne by the society at large

   • If the representatives were selected by sortition, it would be these people that would be using Quadratic Voting every month to decide on what to pass

   • As with referenda, Evaluative Voting is likely to improve consensus building, and permit more fluid political alliances than current de-facto two-party systems

   • A threshold between 2% and 10% of the total possible score should allow things to be passed without too much legislative paralysis

   • With leaders and representatives elected using the methods above, many issues arising from "political capital" are likely to be less prevalent

Of course, it is important not to let the perfect be the enemy of the good. Electoral reform takes time, and the current Plurality/First Past The Post system used in the UK and US is one of the worst ways to do it of all. With that in mind, I welcome the recent initiatives that are seeking to move us away from FPTP, even if they might not be advocating my preferred method. The more things change, the more open to change people become. Therefore, even if the change is only a minor improvement, and isn't to the system that is the best, it can encourage further more rapid change later on.

Now we move out of the simple realm of single offices and single issues. Appointing multiple politicians to represent a population is fundamental to the way in which most modern democracies work, but it is fraught with difficulty.

Proportional Representation (PR) refers to a government whose composition reflects the proportions of the population that support each party. The idea is that if 20% of the population support party A, roughly 20% of the government should be party A, etc.

That proportional representation is a desirable quality in a body of representatives shouldn't be a controversial statement. Any particular demographic being underrepresented within the government will lead to a feeling of disenfranchisement and a loss of faith in the efficacy of a democracy. Alas, there are still a few arguments that are used to try to convince people that unrepresentative governments are somehow a good thing.

Representing Everyone

The main argument against PR seems to be that it results in coalitions rather than outright winners, and that coalitions are weak, ineffective and involve opaque "back-room deals". This is something of a strange objection - firstly, there are many countries that do in fact use PR, and manage to get the job done just fine, so empirically they are not doomed to be ineffective. Secondly, back-room deals happen in every government - they are virtually the entire point of a politician's job. It is hardly as though non-coalition governments can be relied upon to deliver every manifesto pledge without compromise. Aside from this, a good summary of the most common myths around PR can be found on the Electoral Reform Society website.

With the goal of proportional representation, you could divide the country up into small electoral districts that each elect a single politician, trying to keep the "single office" simplicity, but even using Approval Voting, the resulting set of representatives would be unlikely to be a fair representation of the population as a whole. Even in the absence of outright gerrymandering, these systems cannot reliably produce proportional representation, because parties with a moderate level of support that is spread out across a wide area will lose against parties whose support is more locally concentrated:

The 2015 UK General Election was one of the most disproportionate elections on record, but the issue has been know about for much longer than this and has been written about at length. As can be seen above, simulations suggest that IRV (2nd chart), with its single-seat districts does only a little better than the dreadful FPTP (1st chart), resulting in an array of representatives that are nowhere near the proportions that would accurately reflect the actual views of the population (3rd chart). Approval Voting with single-seat districts would be unlikely to fare much better, even if people felt more able to "vote with their hearts", as each individual district would still be a "winner takes all" contest.

Instead, we can look at what is already in use. The main systems that are currently used to deliver a body of politicians that represents the populace proportionately are as follows:

• Mixed-Member Proportional (MMP) used in Germany as well as the Scottish Parliament, Senedd Cymru and London Assembly. CGP Grey has done a good explainer video on how this works.

• Single Transferable Vote (STV) used in Ireland, the Australian Senate and the Northern Irish Assembly. Another CGP Grey explainer video exists for this method.

• Party-list proportional using the D'Hondt method of apportionment, which favours larger parties and is used in Brazil and Austria.

• Party-list proportional using the Sainte-Laguë method of apportionment, which slightly favours smaller parties and is used in Norway and New Zealand.

Unfortunately, despite resolving many of the issues that are encountered when electing representatives, none of these are perfect. They are far superior to the methods used for the UK House of Commons and the US House of Representatives, but this is a very low bar indeed.

The STV method, which is a multi-seat version of IRV, is similarly non-monotonic, meaning that you can harm your candidate by voting for them. MMP and the party-list methods on the other hand place a heavy reliance on political parties themselves, allowing parties to punish politicians for disobedience by moving them down the party list, even if the public supports ideas that are outside of the party's mainstream agenda. Ultimately, all of these are still voting methods that use ranked choices, meaning that they are "ordinal" methods to which Arrow's Impossibility Theorem still applies.

Approvable Improvements

If we can't get a proportional result by using Approval Voting to elect representatives to single-seat constituencies, is there a way to generalise Approval Voting to a multi-seat seat constituency that allows for some degree of proportionality?

The answer to this is yes - in fact there are several. Firstly there is Proportional Approval Voting (PAV), which uses a formula to calculate the "satisfaction" that voters gain from each possible set of winning candidates, and picks the candidates that maximise the population's total satisfaction. This formula gives each person 1 unit of satisfaction for the first winning candidate that they approved, followed by a 1/2 unit for the second, a 1/3 unit for the third etc. Therefore, if there are 5 seats to fill and you approve of 4 of the 5 winning candidates, you are deemed to have a satisfaction of:

while someone that approves of none of them would have a satisfaction of zero. This satisfaction function looks similar to the D'Hondt method of allocating winners in Party-list proportional representation, and in easy to analyse situations it delivers results that are proportional in the way you would expect. For example, in a 3 seat election with 2/3 of people in favour of party A's candidates and 1/3 in favour of party B's candidates, the result would be 2 candidates from A and 1 from B being elected.

Picking the candidates that maximise the population's total satisfaction sounds like a good idea, but unfortunately it is enormously computationally complex. As the number of candidates grows, the number of calculations that must be performed grows super-exponentially, making it undesirable as a system to use on a large scale.

Thankfully, there are two relatively straightforward ways to simplify this system however. The formula to calculate the satisfaction can be simplified, yielding Satisfaction Approval Voting, or the search through the sets of winning candidates can be optimised using what is effectively a greedy algorithm, yielding Sequential Proportional Approval Voting.

Under Satisfaction Approval Voting, if a voter approves of n candidates, each of these approvals is counted as 1/n votes. Sadly, this would discourage people from voting for a large number of candidates, as their "satisfaction" with each candidate would be too small, making it likely that some of their vote would be wasted. This could reintroduce a kind of spoiler effect, in which a group of candidates that are similar to each other could either split the vote between them or cause people to spread their approval too thinly across the group, allowing less popular candidates with more concentrated support to win.

By using the original formula for satisfaction, Sequential Proportional Approval Voting (SPAV) avoids this issue - there is no disadvantage to voting for many candidates. Instead, the candidates are selected sequentially (rather than all at once, as under PAV):

1. The most approved of candidate is elected

2. All ballots that approved of that candidate are reduced in power to 1/2 of a vote

3. With these new weightings, the next most approved of candidate is elected

4. Ballots that approved of this new candidate are reduced in power - either from a full vote to 1/2 a vote, or if already at 1/2 a vote, they are reduced further to 1/3 of a vote

5. Continue in this manner until the required number of candidates have been elected

Although the sequential nature of the ballot counting might miss a slightly more optimal set of candidates that would be found under PAV, it makes for a much simpler process that is also faster to verify. As with any voting method, it is impossible to avoid all tactical voting, but SPAV eliminates most perverse incentives that other systems suffer from. A worked example of SPAV can be found at the Center for Election Science, and further discussion of its advantages can be found here.

I could stop here, with a recommendation that SPAV be used to elect any parliaments or representatives; replacing whichever methods are used currently. Indeed, this itself is probably a hard enough sell. I have however touched on another issue with democracies in a previous post: the pressure on politicians to pander to populism.

Sortition Revisited

The ease with which it is possible to sow division and discord for personal gain is one of the biggest problems that democracies are having to deal with in the current political climate. It is too easy to present a simple solution to a complex problem, and convince people to fall in line behind it. Through no fault of their own, a large number of people can ill afford the time and effort that would be required to inoculate themselves against such tactics.

This means that even with the perfect voting system, there are perverse incentives for politicians themselves. Rather than working together to solve problems, it is in their interest to perpetuate a problem but blame "the other side". Intransigence becomes a virtue and compromise a weakness. The need to win re-election becomes more important to politicians than effective governance, so negotiation is replaced with grandstanding.

The United States Congress has terrible approval (worse than root canal surgery), and yet incumbents are usually re-elected. This is likely to be at least in part because of the incentive for the politicians to "throw the country under the bus" to benefit their particular constituents.

I mentioned a possible alternative approach previously, that I will quote here:

One potential solution to this balance is sortition – the way representatives used to be selected in ancient Athens.  This is a process similar to that used for jury duty, in which a number of members of the public who are citizens in good standing are selected at random to perform their civic duty.  Using sortition to select democratic representatives avoids the rat-race of election or re-election, reducing the pressure to pander to populism.  Its advantages are not simply limited to this however – the representatives being randomly selected from the population all but ensures that the majority of representatives are ordinary people, very much in touch with the wants and needs of the average citizen, rather than out of touch career politicians or technocrats.  Furthermore, given a large enough random selection, it can be made highly statistically likely that the selected people are a good representation of the population at large, which makes it likely that all interest groups are being represented.

It could be argued that since ordinary people do not tend to take the time to understand the nuances of policy normally, this would be a disaster.  However in the case of jury duty it is usual for people to take this civic duty very seriously, and when given leave from their job to perform this function, they have the time to look into any nuances in order to better understand them and make informed decisions.  In fact, there are studies suggesting that politicians that are more open minded and receptive to new perspectives may be less successful at being elected, which may mean that the amount of nuance that politicians are likely to be able to understand is less than that of the average person.

Using Sortition to generate a government body would ensure that it was representative of the population to a far greater extent than any system of voting could hope to do. It would also do away with the pressure of re-election, making the representatives free to compromise and find solutions that might be politically unpopular in the short-term.

This also completely removes the issue of voter apathy - the voters no longer have to vote, they simply have to be available to serve if called upon. In a similar manner to jury duty, the selected people would have to be given a sabbatical from their job, and remunerated appropriately, giving them time to familiarise themselves with the issues facing the government at the time. They would know that their voice mattered and that they only had a limited time to use it, which should incentivise them to understand the issues and do their best to reach decisions that benefitted the country and its people.

The suffrage by lot is natural to democracy; as that by choice is to aristocracy.  The suffrage by lot is a method of electing that offends no one, but animates each citizen with the pleasing hope of serving his country.

Montesquieu, The Spirit of Laws

Duration of Duty

At this point, there is an important implementation detail to consider - how long should these randomly selected representatives serve? Jury duty tends to last for a week or two, unless it is a particularly complex case, but this would be far too little time for a representative to be able to gain an understanding of the issues and have any hope of finding a resolution. On the other hand, members of the US House of Representatives have 2 year terms, so it can reasonably be considered that a representative has a chance to do something productive in 2 years, that can justify them running for re-election. 2 years is a long sabbatical for anyone to take however, so we should consider whether there is anything comparable that we can use to guide us.

Parental leave is a fairly widely applicable "sabbatical" that many people take at some point in their lives. In many countries, laws have been passed and great effort is made to stop companies from penalising or disadvantaging parents for taking parental leave. This is a desirable model, as we don't want a system that disadvantages the randomly selected representatives. Chile, Venezuela, Poland, Czechia and New Zealand all offer around 6 months of maternity leave, and several other European countries offer significantly more, so this is a length of sabbatical that businesses have already adapted to work around. The UK is one of the most generous, offering up to a full year of maternity leave.

Based on this, it would seem that terms of between 6 months and 1 year would be manageable without significantly disadvantaging the representatives or the companies they work for.

This is significantly longer than Jury duty, but it would be quite reasonable to question whether this would still be too short of a time to do anything productive. It takes politicians a while to "learn the ropes", becoming familiar with parliamentary procedure, and with all representatives being replaced every time, there would be a loss of institutional memory on a yearly or twice yearly basis.

I would argue that this is much less of an issue than it might initially appear. Firstly, much of parliamentary/congressional procedure is archaic and unnecessary - much of it revolves around political parties and manoeuvring which would not be relevant under sortition, with representatives that are not answerable to a party. Under the current system, the experience that politicians have in politicking is invaluable - knowing who to hobnob, and how to get leverage over a particular statesperson is essential for getting anything done, but this all becomes much less relevant when all of the other representatives are new as well.

Secondly, a lot of the machinery of government that must be navigated can be done with the assistance of civil servants. The UK government employs large numbers of steadfastly non-partisan permanent staff, who implement the policy of whichever government is in power. These civil servants provide an enormous institutional memory that transcends individual governments, so there is no reason to think that such a system would not cope with a more rapid turnover of representatives.

Thirdly, unlike in a technocracy, politicians in a democracy don't need to be experts - they can requisition experts and advisors for whatever the issue is that they are dealing with. In fact, openness to the advice of experts is an important quality that many politicians unfortunately lack. The role of a politician is to interpret the advice and information they receive, think critically, and negotiate with the other politicians to take actions and pass laws that benefit their constituents and the country as a whole.

Democracy Without Voting

The question we are left with is: is sortition actually democratic? More specifically, can we guarantee fair representation under a system that uses randomness as its driver? This is where we start getting a little statistical, but it is worth it to iron out the wrinkles that are left.

For the sake of having nice round numbers to calculate with, let's assume that we want to select 500 representatives (there are 435 seats in the US House of Representatives, and 650 seats in the UK House of Commons). Let's also assume that our population is nice an evenly split in several different ways: 50% male and 50% female; 50% living in the North, 50% living in the South; 50% urban, 50% rural; 50% over-40, 50% under-40.

If we consider representation to be fair and proportional if it is within 3% of the actual split in the population at large, we would want no fewer than 47% female (or male) representatives, etc., which comes to 235/500.

If we do the simplest thing, and randomly select 500 representatives from the entire population, it initially looks like we are very likely to get a fair representation. There is only a 1 in 6 chance of randomly selecting 500 people from our population, and getting fewer than 235 males or females in our selection. It is possible to see this in Excel using the formula =2*BINOM.DIST(234,500,0.5,TRUE).

The trouble is, we mentioned four different ways that the population could be split 50/50, so we want to select a set of people that fairly represent all of these groups. If each of these splits is independant from one another (i.e. the North isn't predominantly elderly, or the urban areas aren't predominantly female, etc.), this makes it much less likely that we will achieve our goal. With four 50/50 splits, the probability of at least one of these groups having fewer than 235 representatives is slightly greater than 50%. The calcuation here is [latex]\small 1-(1-\frac{1}{6})^{4}=52\% [/latex].

In fact, this gets even worse when the groups of people are smaller, as we end up with even more groups of people that need to be fairly represented. For example, in the UK, only about 2.9% of the population lives in Northern Ireland, so they should receive 14 or 15 of the 500 representatives. The probability of them receiving a number of representatives within the fairly wide range of 11 to 18 is actually only 72% =BINOM.DIST(18,500,2.9%,TRUE)-BINOM.DIST(10,500,2.9%,TRUE).

Thankfully, there is a very simple solution to this - we can keep the rough idea of constituencies and generalise it slightly. If we split the population into groups and select an appropriate number of people from each group at random, this ensures that each group gets the correct number of representatives. For example, a country could be split by age gender and location, giving the following 32 "constituencies":

These constituencies don't have to be exactly the same size, they just need to be large enough to warrant at least 1 representative. If we are representing a population of 50,000,000 with these 500 representatives, that means that each one represents 100,000 people, so a constituency of 400,000 people would need to have 4 representatives randomly selected from it.

Intersecting Identities

There is actually no reason why we cannot break the population down into other sensible groupings to ensure each gets proper representation. Different ethnicities within the population could be constituencies, ensuring that each is adequately represented, as well as different professions, different education backgrounds, parents, and LGBT people.

Clearly if all of these were combined with the 32 constituencies above, this would make an enormous number of individual groups, some of which would be far too small to warrant a representative. There is however a better way to manage this, that avoids this problem.

Let's take medical doctors as an example: Italy and Spain have around 4 doctors per 1,000 people, so in a country with similar healthcare and a population of 50,000,000 we would expect 200,000 doctors. If we want representatives from all backgrounds and careers, in proportion to the population as a whole, we should be aiming to have 2 of our 500 representatives be medical doctors. We don't really need to ensure that both doctors from the North and doctors from the South are represented, or that older doctors and younger doctors are represented. Both doctors being from the North is not an issue as long as the South has other representatives.

If we have the requirement, simply that North and South; old and young; doctors, teachers, farmers, etc. each have a proportionate number of representatives, it is possible to design a system that can reliably select these representatives.

In addition to the demographic groups given in the table above, this system allows us to specify as many other partitions of the population as we would like to represent, as long as every person is a member of a single category within each partition. This means that in the "profession" partition, you can't be in both the "doctor" category and the "teacher" category. Also, it is necessary to have an "unemployed" category within this partition, so that every person gets a category.

A selection algorithm then proceeds as follows:

1. Start with the constituency/category with the smallest number of eligible people

2. Select a random member of this category

3. If this person being made a representative means that any of the categories of which they are a member are now fully represented, all people that are members of the fully represented category are removed from the pool of eligible people

4. Of the categories still needing representatives, take the category with the smallest number of eligible people and repeat until all representatives have been selected

Partitioned Sortition

This may all seem quite abstract, so I shall demonstrate with a worked example. This (somewhat simplified) civilisation consists of 500 people needing 10 representatives. There are:

• 252 men and 248 women

• 219 from the North and 281 from the South

• 45 government employees, 60 unemployed and 395 with private sector jobs

• Three different ethnicities - 49 Jovians, 103 Martians and 348 Terrans

This means that out of the 10 representatives, there need to be 2 men from the North, 3 men from the South, 2 women from the North and 3 women from the South. There also needs to be 1 government employee, 1 unemployed person and 8 privately employed people as well as 1 Jovian, 2 Martians and 7 Terrans.

In the image below, the particular category under sortition is highlighted red. Selected representatives gain a red ring, and people no longer in the eligible pool are greyed out. The partitioned sortition algorithm proceeds as follows:

Working through this step by step:

1. Initially, the smallest category is government employees with a population of 45. One is selected at random, and they are a Terran woman from the South. Government employees only need 1 representative, so this category is exhausted - we remove all remaining government employees from the elegible pool.

2. Having removed these people, the smallest category is Jovians with 44 members (5 of their initial 49 were government employees). One is selected at random, and they are an unemployed man from the North. Both Jovians and unemployed people only needed 1 representative, so both of these categories are exhausted.

3. The smallest category is now "Female, North" with 76 members (the blue dots). One is selected at random, and they happen to be Terran. No categories are exhausted.

4. As no other categories were exhausted, the smallest category remains the same, and another member is selected at random (they also happen to be Terran). "Female, North" only required 2 representatives, so this category is now exhausted and all people that are members of this category are removed from the eligible pool.

5. The smallest category is now Martian with 58 members. The selected representative is a man from the North. There are now 2 representatives for "Male, North" (the purple dots), so this category is exhausted, and its remaining members are removed from the eligible pool.

6. Martian is still the smallest category, so another Martian is selected - this time a man from the South. Martians only need 2 representatives, so this category is now exhausted.

7. The smallest category is now "Male, South" with 75 members (the yellow dots), so one is selected.

8. No categories were exhausted, so the smallest category remains the same and another member of "Male, South" is selected. This is the third representative of this category and only 3 are needed, so all remaining members are removed from the eligible pool.

9. There is only 1 remaining category within each partition of the population - Terran women from the South, in private employment. 2 people fitting these categories are selected at random.

10. We now have 10 random representatives that proportionaly reflect the gender, geographical, ethnic and employment splits of the civilisation.

Pathological Partitions

This is all very well, but is it possible to end up in some sort of bind where the random choices made earlier in the process make it impossible for you to select proportional representatives later?

The two smallest groups in the above example were government employees and Jovians. If instead there was a significant overlap between these two groups, with 40 people being both Jovian and government employees, we can see what would happen when picking the first representative (a government employee):

• If the government employee selected were a Jovian, this person serves as representative for both categories.

• If they were not Jovian, this selection would eliminate all remaining government employees, which would eliminate 40 out of the 49 Jovians. There would then only be 9 Jovians left, which would make them by far the smallest group, guaranteeing that a Jovian representative would be picked next.

Would it be possible to have a variant of this in which there are no Jovians left, leaving them unrepresented?

Well... No. If all Jovians were government employees, and a government employee were picked that was not Jovian that would be impossible. If there were a government employee that was not Jovian, this would mean that the number of government employees was larger that the number of Jovians, so the Jovian representative would get picked first. Alternatively, if all government employees are Jovians too, there is no-one that fits thes criterion of government employee but not Jovian.

This is not a mathematically rigorous proof that such situations are impossible, but it should serve as a sketch for how such issues are avoided by virtue of selecting from the smallest category first.

Verifiability

Another consideration is whether it matters if people's membership in these categories is verifiable, or if people lying about their membership of a category is an issue. If a partition of the population is based around a quality that is hard to verify or based on self-identification, what happens when someone is miscategorised?

I will argue that it is in fact a very minor issue indeed, due to the inherent fairness built into the original concept of sortition before we introduced the partitioning.

Let's take a "worst-case" scenario, in which someone is not just miscategorised, but is in fact malevolently claiming membership of a category in order to stand a chance of selection and subvert their democratic will. By way of an example, we can use the idea of LGBT representation, as membership of this category would be difficult to verify for both practical and political reasons. Out of our earlier hypothetical population of 50 million, let us assume that 2% openly identify as LGBT, which would be 1 million people. This translates to 10 representatives if each represents 100,000 people.

If one homophobic person decided to claim to be LGBT for the purposes of this partitioned sortition there would be a 1 in a million chance of them being selected. Not a very big concern. What if a large number of people did this though - 100,000 homophobic people claiming to be LGBT in a coordinated attack on the democratic rights of the LGBT community?

Well, 100,000 extra people would mean that this category would gain an extra representative. 11 representatives for a category containing 1 million LGBT people and 100,000 homophobes. This works out to give a 35% probability that all 11 representatives would be LGBT =BINOM.DIST(0,11,1/11,FALSE), therefore slightly benefitting the LGBT community by overrepresenting them. There is a further 39% probability of there being exactly 1 homophobic representative =BINOM.DIST(1,11,1/11,FALSE), therefore representing this group perfectly accurately and having no effect on the LGBT community's 10 representatives. This leaves only a 26% chance of there being more than 1 homophobe selected.

Clearly this isn't quite as ideal as when the categories were perfectly delineated, however it is still a vast improvement on the unpartitioned sortition method. Without partitioning, the probablility of such a small group being underrepresented by at least 1 seat is 46% =BINOM.DIST(9,500,0.02,TRUE).

The worst that this situation could get is with a category that is small enough to only warrant 1 representative. If there are fewer than 100,000 people that would be members of a category, it would be inadvisable to split this category out, as although we could round up 60,000 people to having 1 representative, this could encourage a proliferation of tiny categories that would overrepresent certain groups. Further to this, allowing categories with only 60,000 people would mean that 80,000 others could fraudulently join the category, leaving it still with only 1 representative, but with the fraudulent members having a higher chance of being selected than the real members.

If we put a floor of 100,000 on the minimum category size, something similar could still happen, in which just few enough people opt into this category to avoid it gaining a second representative. This would give a situation in which only two thirds of the category were genuine members. This is an unlikely scenario, but is of sufficient concern that small categories that only receive 1 or 2 representatives should ideally be properties of people that are verifiable in some reasonably straightforward way. Categories larger than this are much less of an issue, as demonstrated above.

In the UK

So far this system has been demonstrated with hypothetical populations, but we can now look at a real country and propose a set of partitions that allow us to capture the most representative set of representatives.

The UK has a population of 66.7 million, of which about 55 million are over 16 years old. We can therefore propose a parliament of 550 representatives, each one again representing around 100,000 people. For our first partition, using the 24 "states" suggested in the United Federal Britain post, combined with 4 age bands (under-30s, 30-44, 45-59 and over-60s) and male/female, we get 192 different categories each of which receives between 2 and 4 representatives. The smallest of these categories would probably be women under-30 in "Sussex", with a population around 150,000 whilst the largest would probably be men aged 30-44 in Scotland (around 410,000).

To this we can add more partitions:

These 6 different partitions covering location/age/gender, ethnicity, LGBT status, education status, parental status and employment should ensure a parliament that is truly representative of the electorate. This is not exhaustive though - there is no reason more partitions could not be added, were they deemed necessary or benefical.

Individual Impact

We can calculate the chances of any particular individual being selected over the course of their life. If life expectancy is 85 years and anyone over the age of 16 can be selected, this gives people 60 years of being in the electorate. Assuming people are selected for a 6-month term, this gives them on average 120 chances of being picked.

In 120 rolls of a 100,000 sided die, the probability of getting a 1 is 0.12%, or slightly less than 1 in 800 =1-BINOM.DIST(0,120,1/100000,FALSE). This means that the likelihood of any individual being picked is still very small, but that most people will know a couple of friends of friends that get selected.

Its impact on companies can be calculated too - an employee taking a 6-month sabbatical isn't the end of the world, but it is still a bit inconvenient. If a company has 1000 employees, the probability of having one or more of them be selected in any given year is a fairly manageable 2% =1-BINOM.DIST(0,1000*2,1/100000,FALSE).

One issue to consider when implementing this system would be people that were unwilling or unable to serve. Students with exams and entrepreneurs with fledgling businesses may wish to recuse themselves, and the selection process would need to filter for ongoing mental health issues or cognitive disorders. Neither of these should be problematic on an individual basis, as jury duty already manages these same concerns, however it could become important if a particular category of people within one of the partitions experiences any of these issues disproportionately.

If 50% of the people in a category recuse themselves from selection, this doubles the chances of the remaining people being selected, which could encourage people to fraudulently claim membership of that category. Unlike the example using LGBT categories earlier, this would increase the likelihood of these fraudulent members being selected. As such, this would need to be considered when creating any category within a partition. Any categories with too high a rate of recusal would either be best avoided, or would need some form of verification for members which would increase the administrative burden.

As mentioned above, with only 6 months to a year to familiarise themselves with the issues, formulate an informed opinion, negotiate with their colleagues and implement a legislative decision, this system would rely on civil servants to help this body of ordinary citizens to be effective, and provide a long term institutional memory. This is similar to how the UK's Parliament currently works, so it shouldn't be too unthinkable, but it is still a step into the unknown.

This said, sortition could not be used for the executive branch of the government. Presidents, Prime Ministers, Governors and Cabinets are roles that demand competence and experience. This system would therefore not eliminate all voting, as it would still be necessary to democratically elect anyone that would be given executive power. Voting methods for this have been discussed in a previous post.

When the two forms of election, that by vote and that by lot, are mixed, the first should be used to fill places which require men of special talents, such as military offices; the other, when good sense, justice, and integrity are sufficient, as they are in judicial offices; for in a well-constituted State these qualities are common to all the citizens.

Rousseau, On the Social Contract

Ultimately, it remains to be seen whether a system that selects representatives randomly can be at all palatable to countries that have previously voted for their representatives. At least with the approach of Partitioned Sortition, we can now guarantee proportionality in all fields that are deemed important, rather than leaving it to chance.

For more discussion of Sortition, check out the books Against Elections by David Van Reybrouck and The Principles of Representative Government by Bernard Manin. There are also several communities and organisations pursuing this policy - Democracy Without Elections, the Sortition Foundation and Equality by Lot.

Leaders usually have a significant amount of power, so it is fairly easy to convince people that such elections are important, giving these elections a higher turnout than other elections (for example US Presidential Elections almost always have higher turnout than Midterm Elections). This means that we didn't need to worry too much about low turnouts in the previous section.

This is no longer the case for referenda. Voting has a cost - at a bare minimum, it costs voters the time and effort needed to cast their ballot, and it can cost even more time and effort if a voter wants to become well informed about the issue being voted on. There are therefore several reasons why a large number of people might not vote in a particular referendum:

• They could be unfamiliar with a proposal or an issue, and deem it not worth investing the time in learning about it

• They could be opposed to a proposal but not sufficiently strongly opposed to overcome the cost of voting

• They could be strongly opposed to a proposal but not be expecting it to be popular, resulting in a "tragedy of the commons" like situation, in which people rely on the efforts of other people to vote down a proposal

This results in a risk that a very small number of passionate voters could pass legislation that a large number of people are against.

Thresholds

For this reason, some referenda are implemented with a turnout threshold, such that if fewer than a certain proportion of the electorate vote, the proposal automatically fails and the status quo is maintained.

This leads to its own issues however. If you set the turnout threshold to a level less than 50%, a minority view could be held by a number slightly below the minimum turnout, such that voting against a proposal can validate a result in favour of the proposal. For example, imagine a hypothetical country with a population of 1,000 and a turnout threshold of 40%, where 390 people are strongly in favour of the proposition, and the remaining 610 are against it:

• The 390 people in favour are going to vote for the proposition, so what should the remaining people do?

• They could all boycott the referendum, and it will fail to reach the threshold to be a valid result, meaning that the status quo would continue with the proposition not being implemented.

• If at least 391 of them vote against it, this would mean that the proposition was voted down, meaning that the proposition would similarly not be implemented.

• If however, enough people decided to boycott the vote that fewer than 390 people voted against it, this would be a problem - the turnout would be >40%, validating the referendum, and the proposition would win with more than 50% of votes cast.

• There could be a situation where most of the electorate boycott the vote, but 10 people "don't get the memo" and vote against - these 10 votes cause the threshold of 40% to be reached, resulting in the proposal passing with a 97.5% majority, despite 60% of the electorate being opposed to the proposal, but abstaining from voting or boycotting the vote.

In fact, this issue can occur with an even higher minimum turnout threshold. A threshold of 60% would simply mean that this situation would occur if between 210 and 390 people voted against. The higher the threshold is, the narrower this band is, making this situation less likely, but the possibility of this situation does not completely vanish until the threshold is 100%.

If we decide that we can live with this band being sufficiently narrow, does a high minimum turnout threshold work in other scenarios? Unfortunately not. The problem with having a minimum turnout >50% is that even if something is largely supported, it can be very hard to get people sufficiently motivated to turn out. For example, in the Republic of Ireland, the referendum on the 38th amendment to the constitution was passed with 82% of voters in favour, but turnout was only 51%. If a high threshold such as 60% had been in force, this would not have passed.

Clearly there is an important balance to be struck between allowing minority views to hijack legislation and requiring an unrealistic level of voter engagement, and turnout thresholds are not it. The discontinuity in outcomes that exists around the turnout threshold results in pathological behaviour of the voting system.

Avoiding Discontinuity

Thankfully, this balance can be achieved without such behaviour by using a particular form of our new friend Range Voting. Rather than using a range of 0–4 or the Approval Voting "range" of 0–1 we can use -1–1. This has been given a few names including Combined Approval Voting and Evaluative Voting (EV). By allowing both positive and negative scores, this allows people to vote against propositions as well as voting for them, and gives a convenient way of representing the level of support.

If we use a system that calculates results as a percentage of the total eligible population, and treat a vote of zero the same as an abstention for the purposes of the results, we get the following outcomes:

This means that we can introduce a score threshold without causing the issues described above. If a score threshold of 20% were in effect for the above results, the first row would be a success for the proposition (i.e. nobody cares, except for the 20% of people that want it), but a small number of people voting against it have their votes subtracted from the score, pushing the outcome below 20%, meaning that the proposition fails (in contrast to the turnout threshold above).

In the subsequent rows, it can be seen what proportions of voters for and against a proposition result in its success or failure at a particular turnout. Importantly though, it is never the case that turning up to vote against a proposition would result in a proposition succeeding that would otherwise have failed.

This approach also reduces the divisiveness of very closely fought votes: as can be seen from the second to last line, 52% voting +1 and 48% voting -1 would give a result of "4% in favour" which would not pass a score threshold of 20%, meaning that the status quo would continue until more people could be convinced to switch sides.

The score threshold therefore performs two functions simultaneously:

1. Preventing passage of laws that only a small proportion care strongly about

2. Privileging the status quo in a closely fought, divisive decision

Where to Draw the Line

Exactly what percentage this score threshold should be set at is a very good question, but I am inclined to suggest somewhere between 10% and 50%. For the first function, needing much less than 10% of a population to vote in favour of an issue could lead to situations where it is in a politician's interest to keep publicity of a referendum to a minimum, so that most people don't vote because they're not aware that it is occurring. On the other hand, requiring more than 50% means that the only things that can be passed are things that a majority of the population are already motivated about. Things that certain groups are passionate about, but that the majority are indifferent about would never pass.

Looking at the second function, requiring a score of more than 50% would mean that things would be impossible to pass despite only being opposed by a quarter of the population. Although this might look like it would help avoid a "tyrrany of the majority" scenario, this would likely just result in legislative deadlock that would delegitimise the system and result in its eventual collapse. At the other end of the spectrum, requiring a score of less than 10% would mean that laws could be passed if the votes were 45-55 or closer. In a hotly contested vote, this is likely to cause great divisions within the country's populace. The UK's 4 year long (and counting...) constitutional crisis that resulted from the Brexit referendum is a good example of this, where out of the 46.5 million registered voters, 37.4% voted to leave the EU, 34.7% voted to remain in the EU and 27.8% abstained from voting. This would have given this referendum a score of only 2.7% in favour of leaving, but without any thresholds in place, this was deemed a mandate to deliver an enormous constitutional change. Such a divisive policy being implemented with such a slim majority has resulted in years of political deadlock and acrimony, as well as generating deep divides between different sections of the UK's populace.

This might sound very similar to offering an ordinary vote between a new policy and the status quo, and simply subtracting the votes of one from the other. There is a subtle difference however - by allowing each choice to be scored positively or negatively, two additional features are able to be realised:

• It allows multiple proposals to be compared simultaneously (again with low risk of the spoiler effect). This means that rather than a single option that could be divisive or a poor compromise, many options can be put forward, and the one with the broadest appeal will win (as long as it scores above the threshold).

• It allows a government to determine a proposition's popularity relative to the status quo without having to implement the proposition. If none of the options score above the threshold, the status quo will continue, but if the status quo is itself on the ballot, it may well have actually scored lower than many options. This would be very informative to a government, letting them know that there is a large appetite for a solution. At this point, rather than passing a divisive and half-baked law, a government could attempt to mediate between different interest groups to find a mutually agreeable solution that would have broad enough appeal to pass the threshold.

Of course, there is still no substitute for referenda being well worded and clear. One of the great features of the referenda that are used to amend the constitution of the Republic of Ireland is that they are votes on whether or not specific wording should be added to (or removed from) a document. The law being changed is clear, and the way in which it is changing is clear, so there is no room for ambiguity in the interpretation of the people's wishes.

Using Evaluative Voting, multiple proposals to address the same issue could be put forward and voted on in a single referendum, but each proposal really should be well formed, to avoid confusion. Any referendum that is not asking about specific wording for a specific law is asking for trouble. This can be seen by the endless discussions and recriminations about whether the "will of the British people" was to [join the EFTA]/[continue within the ECJ]/[enter into a customs union] after leaving the EU (delete as appropriate). A referendum is not an opinion poll, and should be invoked with the same care and attention that any other election is due.

Perhaps in very small groups, consensus building can be used to bypass the need for voting, but as groups of people get larger, the number of possible disagreements to resolve and compromises required to reach consensus grow rapidly. This is one of the reasons why teams within a company are generally recommended to be smaller than 20 people, with 5-7 often being considered ideal.

Given that no country is this small, the need to implement a system of voting is something of an inevitability. Unfortunately, there are many ways in which voting systems can introduce issues that stand in the way of the democratic process. Issues such as gerrymandering, hyper-partisanship and voter apathy are often a direct result of the system that is used.

Without consensus building being strictly required, voting introduces the risk of Tyrrany of the Majority. Judicial systems are therefore a critical component of modern democracies, which serve to protect minority voices, but it is an imperfect system - there is no rule of law that cannot be replaced by a large enough majority. In the end though, even a consensus based system in a tiny community isn't immune to this - a large enough majority that is sufficiently well coordinated could just decline to find a consensus, and kick out the minority (or worse).

With this caveat established as unavoidable however, there are still a great many other issues evident in the voting systems of most modern democracies that should be able to be improved upon.

Different Purposes

Quite apart from voting methods themselves, there are four very different purposes for which voting can be used:

1. Leaders (Presidential/Gubernatorial Systems)

   • People voting for the leader of a nation, state, department or entity

   • These are "single seat" positions - there may be multiple people running for the office, but only one can win any particular office

2. Referenda (Direct Democracy)

   • People voting directly on specific issues or laws

   • Can be yes/no questions, or a choice of more options depending on the approach

3. Representatives (Representative Democracy/Parliamentary Systems)

   • People voting for representatives to pursue their interests in the corridors of power

   • The combination of politicians that are appointed are supposed to be in some way representative of the population

4. Procedures (Intra-governmental decision making)

   • Politicians within a representative democracy use voting to decide on issues and to pass laws

Although on the face of it, these four purposes could be considered very similar (and indeed are treated similarly in most democracies), they each encounter very different issues. If we are to try to improve on existing approaches, it will be worth separating them out, and considering each of them on its own.

In this post, I shall focus on the first of these, with the other three following in posts of their own.

Electing Leaders

Electing someone to a single, stand-alone office such as a president or a governor is usually is a fairly common goal and as such, much ink has been spilled over the best way to do this.

Unlike with representatives, the stand-alone nature of the office makes certain potential pitfalls very simple to avoid. To implement a system for something like a presidential election that manifests any kind of gerrymandering-adjacent issues, takes... effort (I'm looking at you, US Electoral College). Just because some countries fail to meet even this very low bar doesn't mean that we can't set the bar higher.

In a straightforward vote to determine the winner of a single office, the main thing standing in the way of getting a leader that best represents the interests of the electorate is tactical voting. Any vote with more than 2 options is open to tactical voting, but there are some forms of tactical voting that are more pathological than others. A bad voting method will provide perverse incentives that result in people that support a particular candidate voting for someone they support less, or not voting at all.

The really problematic issues that voting methods could have, that it would be good to avoid are the following:

• Being a dictatorship

  • This one is obvious - if there is someone whose vote always determines the winner, it is de-facto a dictatorship, not a democracy, so this is a pretty undesirable quality

  • A voting method that avoids this is referred to as a "Non-dictatorship"

• Permitting only one axis of satisfaction

  • Imagine an election between four candidates with the manifestos:

    1. "Crush our enemies, save the environment"

    2. "The best defence is a good offence, tax polluting industries"

    3. "Avoid conflict, stop worrying about the climate"

    4. "Get rid of the military, burn the forests"

  • Despite the presence of two very different issues, these four candidates are on a single axis from one extreme to the other

  • There is no party for non-interventionist environmentalists or for interventionist industrialists

  • A voting method that permits any combination of preferences is referred to as having "Unrestricted Domain"

• Changing the winner when an additional unpopular candidate runs

  • Clearly if an additional candidate is very popular, they could win the election, but if the additional candidate isn't going to win, their presence in the election shouldn't change who does

  • A good example of this from the sporting world is the 1995 women's figure skating world championships, in which the performance of the fourth place finisher resulted in the competitors in second and third switching places!

  • This phenomenon also includes the "Spoiler Effect", in which a candidate splits the vote of the candidate that would have won, resulting in the second most popular candidate winning instead

  • A voting method that is unaffected by the presence of irrelevant candidates is said to have "Independence of Irrelevant Alternatives (IIA)"

• Declaring a victor that voters unanimously rated worse than another

  • If all voters prefer candidate X over candidate Y, the voting method should not result in candidate Y doing better than candidate X

  • A voting method whose result always preserves unanimous preferences is referred to as "Pareto Efficient"

• Reducing a candidate's performance when they get more votes

  • If the act of voting for a candidate, or ranking them higher causes them to perform less well, this is clearly a perverse incentive that could discourage people from voting honestly

  • Equally, being able to improve a candidate's chances by voting against them is a problematic tactic to encourage

  • Despite its simplicity, the Single Transferable Vote method can result in situations where this occurs

  • A voting method in which support will never harm a candidate's result is referred to as "Monotonic"

(Site note: there are criticisms of having IIA as a requirement of a voting method, insofar as it is in direct opposition the Majority Criterion (that if a candidate is the favourite of a majority of the electorate, then this candidate will necessarily win). Whilst the Majority Criterion sounds like an obviously desirable quality of a voting method, it is worth considering the issue of Tyrrany of the Majority alluded to earlier. A compromise candidate that is not the majority's absolute favourite, but that has the support of an even broader section of the electorate is generally going to be less partisan and more of a unifying force. This makes the Majority Criterion actually not such a "no-brainer".)

So, having decided on a very reasonable set of minimum requirements to have for a voting method, so that we avoid obvious failure modes and perverse incentives what are we left with?

Well... Not much actually! It turns out that it can be mathematically proven that it is impossible to design a ranked preference voting method that satisfies all of Non-dictatorship, Unrestricted Domain, IIA, Pareto Efficiency and Monotonicity. This is known as Arrow's Impossibility Theorem, and it is indeed most disappointing.

Cardinal Virtue

Do we now give up and go home? Is how we decide our leaders doomed to be hopelessly broken in some way? Not quite yet. There is a glimmer of hope in the previous paragraph where the statement of Arrow's Impossibility Theorem includes the words "ranked preference voting method".

A large number of voting methods involve people ranking the candidates in order of their preference, so they pick who their 1st choice is, who their 2nd choice is, and so on. You can't rank multiple candidates as 1st, even if you consider them indistinguishable. These are also known as "ordinal" voting methods, and for a long time, this was the default assumption when people were trying to find ways to improve how to reflect people's wishes through voting.

There is another way however - "cardinal" voting methods are ones in which you give candidates a score which doesn't have to be unique. Giving a higher score to a candidate means that you prefer them - simple! This change in approach means that Arrow's Impossibility Theorem no longer applies, which is a huge win.

So which voting methods does this leave us with? For the kind of single winner elections we are looking at here, there are a few alternatives:

Range Voting (or Score Voting) involves giving voters a range of scores that they can give to candidates - perhaps 0–4, 0–10 or even -100–100, then allowing voters to give all candidates a score in this range. These scores are then added up, and the highest scoring candidate wins. A good summary of Range Voting and its nuances can be found here.

Approval Voting is really just Range Voting with a range of 0–1. You can either approve of a candidate or not. This does inevitably reduce the amount of information a voter can give the voting system, but it has the advantage of being much easier and simpler to implement. You can use the same voting slips as are used for current "first past the post" elections, but people can put a cross in as many boxes as they want. There is in fact a charity in the US aimed at promoting Approval Voting, whose website has more information about its benefits.

Majority Judgment is similar to Range Voting but instead of summing the scores and picking the highest scoring candidate, the candidate with the highest median score wins instead. This has the effect of discounting extreme outliers, making certain types of tactical voting less effective, but with the cost of making the process slightly less simple and understandable.

STAR Voting stands for Score Then Automatic Run-off. This is Score/Range voting in which all but the top two candidates are eliminated, then the winner is the candidate with the most ballots scoring them higher than their opponent. This method has demonstrated resistance to tactical voting in simulations, though the introduction of an automatic run-off actually results in this method still failing IIA.

Unfortunately for Majority Judgment and STAR, they both fail a couple of other very reasonable criteria that have not been mentioned yet, as they are not covered by Arrow's theorem:

• They both fail the Participation criterion, which means that there are situations in which voters can do better by not voting. This is not quite as bad as non-monotonicity, but it is a very similar problem that could make the methods appear undemocratic.

• They both also fail the Consistency criterion, which means that if the electorate is split into parts, even if all of the parts have the same winner, a different winner can be elected by the combined electorate. This could lead to some very confusing maps being produced that shake people’s faith in the legitimacy of their democracy.

Reliability

With all of these cardinal methods, it is still permissible to vote for a single candidate, if that is the only candidate you approve of. Equally, if you approve of all but one candidate you can vote for all but one (in the case of Approval Voting, this has the same effect as cancelling out one vote for that candidate). Anything between these two extremes is completely fine too, allowing you to not worry about "wasting a vote" on a small party that doesn't have much chance. This should allow people to vote with their hearts much more, reducing the stranglehold that two-party systems have over most "first past the post" democracies.

Of course, it is important to note that this doesn't completely remove tactical voting. In fact, Gibbard's Theorem states that there will always be possible scenarios in which tactical voting can be beneficial to voters, so cardinal voting methods are not immune. For example, Burr's Dilemma is a potential issue that could still arise if two quite similar candidates are also frontrunners, though there are hardly any examples of this occurring in practice. Large numbers of voters practicing tactical voting in a Burr's Dilemma type situation will break IIA, because even though voters' opinions shouldn't change, the tactics being used change depending on which candidates are running.

Range Voting and Approval Voting do however satisfy all of the conditions above when people vote honestly - Non-dictatorship, Unrestricted Domain, IIA, Pareto Efficiency, Monotonicity, Participation and Consistency. This means that you are never punished for participating (voting for your candidate can't hurt their chances), and the spoiler effect is avoided for minor candidates (there is no vote-splitting, unless the "spoiler" themself is a major contender, leading to Burr's Dilemma style tactics). This should reduce political polarisation by making voting for centrist parties more attractive, as well as increasing engagement by making voting for niche parties more attractive too.

All of this makes these methods significantly more reliable than most other voting methods for actually capturing the preferences of the populace. The graph below shows the hypothetical outcomes of 144 simulated elections, where the outcome is measured by the average satisfaction the electorate has with the election winner (known as the Social Utility Efficiency or Voter Satisfaction Efficiency):

(Side note: for Approval Voting, Range Voting and Majority Judgment to satisfy the IIA criterion, it is assumed that voters' individual scores themselves are also independent of irrelevant alternatives. This assumption implies that in an election with only two candidates some voters might vote for both (or neither), which would be a vote that had no effect. I am inclined to think that this is completely reasonable, after all plenty of people currently choose not to vote because they don't approve of any of the parties. Further to this, in the case of only two candidates, most of the issues that plague voting methods are avoided anyway, and many different methods become equivalent to each other with only two candidates in the running. Finally, part of the benefit of these particular voting methods is that they encourage more than two candidates to run, so this situation should not be the norm.)

Recommendation

Of the cardinal voting methods discussed, I am personally inclined towards Approval Voting for these purposes, due to its greater simplicity and familiarity when compared to current ballot papers. Nicky Case's website has a brilliant, interactive introduction to voting methods, the issues with ranked voting and the benefits of Approval Voting. Even if you are already quite familiar with the issues discussed here, I highly recommend checking it out.

Click here to skip straight to the section on Germany or to Canada.

Once a country is already federal, it is much more difficult to make any sort of changes to either the structure of government or the states themselves - this is part of the point of federalism after all. It is still worth considering what changes could be made, whether they would be a desirable way of solving certain issues, and whether they would be able to garner enough support to be achievable.

As with the UK in the previous posts, I shall therefore detail a possible structure for Canada and Germany that follows the same principles. This is not intended to be a serious policy proposal, as such a change would need broad support from the populations affected, as well as buy-in from the existing state governments in order to make the necessary border adjustments and constitutional amendments. This is in contrast to the UK, which would simply need a government so inclined, and a population that wasn't violently opposed to it.

I considered doing the US as well, but decided against it, as the political polarisation is such that any such proposal would probably be taken too seriously and end up offending everyone. Therefore, without saying too much I shall simply set out my starting point for the US, and let people extrapolate from there.

• Alaska is a unique environment within the US and borders no other states, so cannot easily have its borders adjusted to increase its population. It has a relatively small population of 731,000 so this could be the limit for the smallest state.

• This makes the maximum size of a state eight times the population of Alaska, which is 5,850,000 - roughly the size of Wisconsin, the 20th most populous state.

• As a minimum, this implies that the largest 19 states would need to be either adjusted or split into multiple states.

• Wyoming, Vermont and Washington D.C. are all smaller than Alaska, so would also need to be adjusted or combined with other states.

• The aim of splitting large conurbations off into their own states would at the very least need to cover New York, Los Angeles, Chicago, Washington, San Francisco, Boston, Dallas-Fort Worth, Houston, Philadelphia, Miami and Atlanta, each of which has a Combined Statistical Area that covers a larger population than the maximum population of 5.85 million.

• The urban states wouldn't necessarily have to cover the entire CSAs of all the cities above, as some of the areas included in the definitions are fairly distant suburbs, so some of them could squeeze into single states (e.g. the bit of the Washington metropolitan area that is inside the capital beltway has a population of around 2.8 million), but others would require multiple states, for example even just taking the bit of the New York-Newark metropolitan area inside of I-287 would give a population over 16 million.

I think that is more than enough to upset everyone with the possible exception of people from Alaska and Wisconsin, so I'll move on.

Germany

Germany is one of the easier countries to apply these rules to, as its Länder are already relatively close in size - Nordrhein-Westfalen has only 26 times the population of Bremen!

There isn't the same issue that the US has with Alaska - none of the small Länder are quite so difficult to increase in size, so we can aim for a range of sizes that is slightly larger than the one proposed for the US above.

The smallest of the Länder is the "Free Hanseatic City of Bremen". Merging it with a much larger more rural region would likely be unpopular, as it is currently a city-state and would lose a lot of autonomy under such a proposal. Thankfully it borders the historical "Duchy of Oldenburg" which contained the cities of Oldenburg, Delmenhorst and Wilhelmshaven. Combining Bremen with Oldenburg gives a region with a population of 1.6 million, at least 1 million of which live in the aforementioned cities, allowing it to retain a reasonably city-state like character.

The next smallest is Saarland, which also has a unique character given its history as a French protectorate. Merging it into a significantly larger region therefore would also be very unpopular. Extending Saarland slightly Northwards to include the city of Trier, and Eastwards to include the towns of Zweibrücken and Pirmasens gives a region with a population of 1.4 million, whilst hopefully still maintaining its character.

Taking this as the new smallest region gives us a largest permissable state of 11.2 million, which is large enough to not necessitate completely redrawing everything (unlike the US). In fact, to meet the size restrictions, we would only technically need to split Nordrhein-Westfalen and Bayern in two. Taking composition into account does push us towards making slightly more extensive changes than this though.

Firstly, aside from the existing city-states of Berlin, Hamburg and Bremen, there are several other large cities that could be split off into autonomous city-states in their own rights. These are:

• Frankfurt

• Stuttgart

• München

• The polycentric Rhein-Ruhr conurbation containing

  • Dortmund

  • Essen

  • Duisburg

  • Köln

  • Bonn

By taking the area around each of Frankfurt, Stuttgart and München that includes most of their metropolitan area, we get three city-states of reasonable sizes - between 2.3 and 2.7 million people each. On the other hand, the entirety of the Rhein-Ruhr conurbation's metropolitan area would cover most of Nordrhein-Westfalen, so taking only the core, densely populated districts is preferable in this case. This gives a city-state of 8.2 million people - large, but well within the permissable limits.

After carving out these cities, we need to tidy up the other borders - among other things, the Rhine-Ruhr conurbation has left Nordrhein-Wesfalen with a huge hole in it:

• The Western part of Nordrhein-Westfalen can be combined with Rheinland-Pfalz, the Eastern part with Hessen, and the Northern part with Niedersachsen

• Niedersachsen is then very large, so can be split West-East into Westfalen and Hannover

• Rheinland-Pfalz is also quite large, so can be split into Rheinland to the North-West and Pfalz to the South-East

• Pfalz can be extended into Baden-Württemberg, to include Mannheim, Heidelburg and Karlsruhe, forming a moderately densely populated region of many small cities (covering a similar area to the old Bavarian district of Rheinkreis)

• Bayern is still too large, so its Northern districts of Oberfranken, Mittelfranken and Unterfranken can be split off to form Frankenland (along with the bit of Baden-Württemberg to the North-East of Stuttgart)

• Thüringen and Sachsen-Anhalt are quite demographically similar and relatively small, so can be combined, along with a few other minor border changes

These adjustments result in the following map:

We have increased the number of Länder from 16 to 21, but now Rhein-Ruhr (the largest) is only 5.9 times the size of Saarland (the smallest), and there are between 6 and 8 city-states, depending on how you classify Bremen-Oldenburg and Pfalz.

Also, in case is wasn't already obvious, I am a big fan of self determination. I fully support the residents of each region being able to vote on what they call themselves, so if you don't like the names here, feel free to change them!

Canada

Canada is on the other end of the scale - including its territories as well as its provinces, Ontario has over 360 times the population of Nunavut.

On the one hand, if we took Nunavut and Yukon Territory to be the minimum permissible province size, the maximum at 8 times this would be a population of only 288,000 which would require Canada to be split into in excess of 130 different states.

On the other hand, autonomy for Nunavut was a long awaited development, and was largely welcomed by the Inuit community. To reduce its autonomy by combining it with other areas would likely be an unpopular move.

Thankfully, the idea of semi-autonomous subdivisions is probably helpful here. Currently, the provinces are considered sovereign whilst the territories only have delegated authority from the federal government. If done correctly, the creation of a new province would not have to diminish the autonomy of any current territory - shifting powers from the federal government to the new provincial government without shifting powers from the subdivisions to the provincial government. This would allow the former territories the same level of autonomy as before (presumably greater autonomy than subdivisions of other provinces), whilst providing the federal government a larger entity to interact with.

Even with this, it seems likely that the sparsely populated North will be the province with the lowest population and will therefore constrain the maximum permissible provincial population. This then raises the question of how high we can get the population of this Northern province whilst adhering to the idea that it should have a relatively consistent character, maintaining its property of having a very low population density so that it doesn't have to deal with the needs of any sizeable cities.

As it happens, the Northernmost parts of British Columbia, Alberta, Saskatchewan and Manitoba are very sparsely populated, and would not be out of place in such a province. Nord-du-Québec and Labrador also have a very low population density in general, and a significant Inuit population in the areas of Kativik and Nunatsiavut respectively.

To make it easier to discuss, I am going to refer to this province as Borealia (after all, it does contain a large amount of the boreal forest). As with Germany, any names mentioned here should be considered placeholders. We can finesse the borders of the province later, but for now, to give an idea of the population size that we can easily achieve, let's add up the populations of all of these territories and districts:

With a combined population of 308,000 we can call this our minimum province size, which limits our maximum size to 2.46 million.

We will come back to this Borealia later, and deal with the question of subdivisions, but first let's try to work within the above constraints, and see what provinces are possible.

Firstly, there are 5 cities in canada with a population over 1 million, making them easily large enough to be provinces in their own rights:

• Toronto

• Montreal

• Vancouver

• Calgary

• Edmonton

Calgary and Edmonton are both surrounded by a few smaller population centres, which make the areas around them slightly more densely populated than most of the rest of Alberta. If these regions are carved out into their own provinces (each with around 1.5 million people), this almost splits Alberta into two, making it reasonable to divide the remaining area of Alberta into a North-Westerly province (I will refer to this as Jasper, as it contains Jasper National Park) and a South-Easterly one (Alberta), each of which contains around 500,000 people - well within the size constraints.

Vancouver is a significantly larger city, so its metropolitan area can be split from British Columbia forming a densely populated province of over 2 million people. To its East is a commuter corridor sandwiched between the Fraser river and the border with the US, which can also be split from the rest of BC forming another state of around 500,000 people (Chilliwack). Another very straight-forward division would be to make Vancouver Island its own province of around three-quarters of a million people (Nanaimo), leaving the rest of British Columbia with just over 1 million.

Moving further East, having already transferred the very sparsely populated Northern districts of Saskatchewan and Manitoba to Borealia, they both have a fairly even population density, and populations slightly over 1 million, so need no further adjustment. The next province we reach is Ontario, but from Kenora all the way to Algonquin Provincial Park is exceedingly sparsely populated, making it sensible to carve off Northern Ontario into another province of around three-quarters of a million people (Huron).

Southern Ontario is still far too large at almost 13 million people, and whilst we might intend to split Toronto into a separate province, even the core of the City of Toronto clocks in at 2.7 million people which is slightly too large. Excluding the district of Scarborough to the East leaves Toronto with 2.1 million people, then the remainder of the Golden Horseshoe can be split into 3 provinces - Scarborough to the North and East of Toronto, Mississauga to the West and Niagara to the South (across Lake Ontario).

Chopping the Golden Horseshoe out of Southern Ontario removes its most densely populated areas, but still leaves over 5 million people in the region, meaning that it will need to be split into at least 3 provinces to come within the population thresholds. From West to East, I shall refer to these as Erie, Ontario and Ottawa.

The Francophone province of Quebec is up next, with a population of over 8 million (even after having removed the district of Nord-du-Quebec, which makes up over 50% of its area). As mentioned above, Montreal can be made into its own province, and as it is on an island, the most natural boundary for this province is the river splitting the islands of Montreal and Laval from the rest of Quebec. This gives the province of Montreal a population of 2.4 million - just under the threshold.

The St. Lawrence River divides Quebec into a North and a South, with the South being significantly more densely and more uniformly populated. It therefore makes sense to split this Southern region off to form its own province (Appalaches). The remaining Northern part of Quebec is still too large to be a single province, so can be split into an East and a West province. The West province (Laurentides) consists of the valleys directly North of Montreal - a tourist destination known for outdoors pursuits, while the East province (Quebec) contains Quebec City itself along with Saguenay and the coastline of the Gulf of St. Lawrence. This results in 4 Francophone provinces, meaning that the lone French voice in the Council of the Federation will no longer be alone.

Finally we reach the Atlantic Provinces. New Brunswick is the only province that is officially bilingual English and French - two thirds of its population of three-quarters of a million people speak English, while one third speak French. As it happens though, the new province of Appalaches is slightly too large, and the Gaspé peninsula along with the Southern shore of the St. Lawrence Estuary that border New Brunswick are significantly less densely populated than the rest of the province. Moving this region from Appalaches to New Brunswick reduces the population of Appalaches to 2.3 million whilst increasing New Brunswick's to just over 1 million, making the proportion of French speakers in New Brunswick close to 50%.

Prince Edward Island is a very small province that is below the minimum threshold, so it can be combined with Nova Scotia (which has a similar population density). If they are to be part of the same province, it might also be sensible to shift the border between Nova Scotia and New Brunswick slightly to the West, so that the Confederation Bridge is part of Nova Scotia too. This increases Nova Scotia's population to just over 1 million.

With Labrador moved to be a part of Borealia, Newfoundland is now on its own. Having a population of just under 500,000 places it well within the tolerances, so it can quite happily be its own province. Furthermore, as a populous island, it makes sense for Newfoundland to have autonomy rather than be ruled from a capital a boat-ride away, similar to Vancouver Island/Nanaimo.

This is mostly it, aside from a few minor border adjustments. As the Western border of the former Alberta, Jasper's Western border follows the limit of the Nelson River drainage basin followed by the Mackenzie River drainage basin until it hits the line of longitude 120° West. Instead of going directly North at this point, Jasper could be extended further Westwards, continuing to use the Mackenzie River drainage basin as its border until it meets with Borealia.

In a similar vein, Borealia's Southern border would be a fairly messy affair if it used the borders of the districts given in the table above. Instead, watersheds can be used, giving a more pleasing borderline.

Borealia does not yet include any of Northern Ontario (now Huron), despite incorporating parts of Manitoba and Quebec on either side. Even relative to Huron's low population density, the Northern areas are extremely remote and sparsely populated, making them a more natural fit with the rest of Borealia than with the rural but accessible Southern part of Huron, which includes Thunder Bay, Timmins and Sudbury. Kenora District and Cochrane District both extend too far South to be able to move them into Borealia in their entirety, but using a combination of watersheds and the census boundaries of settlements on the ON-11 highway, a large area with a tiny population can be carved out of Huron. This allows us to increase the population of Borealia slightly, making Montreal less close to the upper threshold of 8 times the smallest province.

The proposed province of Ottawa has similar borders to the region of Eastern Ontario, which has a Francophone population of around 270,000. As well as having a large Francophone presence, it contains the federal capital of Ottawa, so making it another province with both English and French as official languages is hopefully not an unreasonable concept. The Regional County Municipality of Vaudreuil-Soulanges is separated from the rest of Quebec by the St Lawrence River and the Ottawa River, but it shares a land border with the new province of Ottawa. By incorporating this municipality into a bilingual Ottawa instead, it would add another 100,000 French speakers, making the province of Ottawa over 20% Francophone, as well as yielding a more natural boundary between the provinces.

With this, we can see the final 26 provinces that have been laid out. They are shown below, overlaid onto the same population density map as before:

Even zoomed in, several of the states are a little on the small side, so here are some close-ups:

As per the table below, you can see that the most populous province (Montreal) has 6.5 times the population of the least (Borealia). In terms of area though, Borealia is over 15,000 times the size of Toronto.

Borealia

As mentioned earlier, it is worth looking more closely at Borealia, as the existing territories are very likely to want significant autonomy within the province itself. This proposal therefore needs to incorporate details of Borealia's semi-autonomous subdivisions in order to avoid giving the impression that the territories would be completely subsumed and might lose their existing autonomy.

There are four groups of indigenous languages present in the area covered by Borealia:

• The Cree dialect continuum (orange), which has 117,000 speakers

• The Ojibwe dialect continuum (red), which has 56,000 speakers, 48,000 of whom are in Canada

• The Inuit dialect continuum (blue), of which Inuktitut is the most prevalent dialect in Canada with around 40,000 speakers

• The Athabascan languages (green), of which Dënësųłinë́ (also known as Chipewyan) is by far the most prevalent with around 12,000 speakers, followed by Slavey (2,100 speakers), Tłı̨chǫ Yatıì (also known as Dogrib, 1,700 speakers) and Gwich'in (500 speakers)

It is apparent that Ojibwe is mostly too far south to be relevant, with most speakers residing in Huron and Laurentides. Also there is little presence of indigenous languages in most of Yukon Territory. This suggests that the four language groups of Cree, Inuit, Athabascan languages and English could be used to define districts.

This aligns with the motivation behind Nunavut becoming its own territory, allowing the Inuit communities a greater degree of self-determination. Currently the Northwest Territories have 11 official languages however, which include 3 Inuit dialects as well as French and Cree. With so many languages each of which with so few speakers, this presents a risk that language resources may be spread too thinly, making preserving the languages more difficult.

By splitting Borealia more carefully along linguistic lines, it should be possible to create autonomous subdivisions that each have a smaller number of more dominant indigenous languages, allowing greater focus on preserving both language and culture. Using watersheds, I have divided Borealia into 5 districts:

• Yukon - largely English speaking with little indigenous language presence - Yukon River basin and Northern BC

• Nunavut - all Inuit communities including Northern Quebec and Labrador - Arctic drainage basin

• Athabasca - largely English speaking but with significant Athabascan language communities - most of the Mackenzie River basin

• Algonquia - Cree communities in Saskatchewan, Manitoba and Ontario

• Labrador - Cree communities East of James Bay - separated from Algonquia to avoid a long, thin district that would be difficult to administer

The map below shows all of the settlements in Borealia with more than 1,000 residents. Nearby settlements that are separate for census purposes are counted together:

The 80 settlements shown on this map account for about 250,000 of the total 370,000 people in Borealia, meaning that one third of the population of Borealia live in remote settlements of less than 1,000 people. Of these 250,000 people, about half live in the largest 13 settlements:

Final Proposal

To better see the borders of the 26 provinces (and the 5 semi-autonomous subdivisions), I have again produced a zoomable overlay on Googlemaps.

Having changed all of the borders it would make sense to tidy up all of the counties. As mentioned in Legibility and Democracy, the current state of the UK's administrative areas is a mess. Some areas are two-tier counties that have a county council as well as multiple district councils within them, while other counties are purely ceremonial and have no government function, having been split into rural and urban unitary authorities. To make matters even more confusing, some counties are two-tier, but with some districts carved out of the original ceremonial county to be unitary authorities not governed by the county council itself (e.g. Nottingham and Nottinghamshire).

In the following map, I have split each state into unitary authorities, so that there is a single consistent level of government below the state government. In a similar manner to with the states themselves, I have tried to separate urban and rural areas into separate authorities, so that local government can also avoid the pitfalls of having to cater to constituents whose requirements are too much at odds with each other.

Clearly the states themselves should have the powers to adjust their internal divisions as they see fit, rather than being handed them by the federal government, but if we are creating the states from scratch, we can at least give them sensible divisions to start with. In fact, given the issues that the US has with local government, it is apparent that managing the borders of local administrative areas cannot be permanently devolved below the level of the state. If local governments (below state level) are given some degree of control over their own borders, there needs to be a way for the state government to step in when populations change too much or their existing layouts become pathological. A similar kind of approach to the proposal for adjusting states within a federation may work for this.

These administrative divisions are referred to as "cities" for urban areas of rural states (coloured cyan), "counties" for rural areas of rural states (coloured green) and "boroughs" for areas of metropolitan states (coloured blue):

These 256 divisions consist of 85 Counties, 50 Cities, 109 Boroughs and 12 special districts. Aside from the special districts that I will mention briefly below, all 244 counties, cities and boroughs have a population between 125,000 and 400,000. Population information can be seen on the map below by clicking the relevant area.

This is in stark contrast with the current situation in which there are 404 principal local authorities in the UK - 25 county councils, 188 district councils, 56 unitary authorities, 36 metropolitan boroughs, 32 London boroughs, 32 council areas in Scotland, 22 principal areas in Wales and 11 local government districts in Northern Ireland, as well as the sui generis Council of the Isles of Scilly and the City of London Corporation. The unitary authorities alone vary in size from Cornwall with 570,000 people to Rutland with 40,000, whilst the largest metropolitan borough is Birmingham with 1,100,000 people and the Isles of Scilly have a population of just over 2,000.

Brief side-note on "Special Districts":

• The special districts are smaller in population (21,000 to 100,000) and are coloured orange on the map.

• They consist of central London (London, Westminster, Bloomsbury, Southwark, Docklands), Northern Scotland (Orkney, Shetland and the Outer Hebrides), Penwith (including the Isles of Scilly), Jersey, Guernsey and the Isle of Mann.

• These 12 exceptions are due to their unique nature, for which it is probably beneficial for them to have their own local governments despite their small size.

• The 3 sets of Scottish islands each need their own local councils due to how far they are away from each other, despite their small populations.

• Penwith includes the unique Isles of Scilly whose requirements could be overlooked if it were combined into an area that dwarfed them too much. On their own, the Isles of Scilly make up around 0.1% of the population of Kernow, so keeping them as a district by themselves would both involve the Kernow state government having to deal with a tiny authority which would be quite inefficient, as well as having the local authority itself being comparatively large with respect to the population it serves. This district is then aimed at finding a middle ground between being so large that the Isles unusual requirements are overlooked, and so small that the authority becomes a burden on both the citizens and the state government.

• Central London's 5 special districts have been kept small because of the sheer number of companies registered there. Just as addressing people's concerns becomes more difficult as the number of people increases, the same is true of companies. This also avoids a single local authority having too much influence over the large economy of central London.

• The crown dependencies of Jersey, Guernsey and the Isle of Mann are exceptions because they currently have independent governments, and any attempt to combine them properly into a United Federal Britain would likely require an element of independent government to continue.

• I have placed the Isle of Mann into Rheged and the channel islands into Solent because they are all far too small to be states in their own right, but if their integration could be achieved, they would likely retain more autonomy within their respective states than an ordinary district.

With these administrative divisions (listed in full at the bottom), it might look like I have used a cut-off of 750 people per square kilometre between something being a county and being a city. It is not just an arbitrary cut-off though. The least dense cities (Blackburn, Cambridge and Newport) still have city-like characters, with a main centre, some satellite towns and some less dense suburbs or countryside around them. This is in contrast to the most dense counties (Windsor and Hertfordshire) which have a much more even distribution of towns, giving a more decentralised character. With this approach in mind, I have tried to adjust the borders of the cities and counties to generate a sensible structure with cities and counties having both different characters and being on different sides of a population density cut-off.

I have uploaded the map above to Google Maps, allowing it to be overlaid on top of a zoomable map of the UK.

Cities and Counties

The UK currently does not have a population based metric for determining whether something is a city, preferring instead to confer city status by virtue of having a cathedral, or manually on an ad-hoc basis. Accordingly, there are several tiny cities on this list that no longer make the cut (e.g. Truro, Bangor and Ely), and several cities that I outline that were not on the list (e.g. Telford, Luton and Milton Keynes). It is important to note however that some of the "official cities" on the list linked above have extremely generous borders, that include a large amount of countryside. The actual urban areas of Chelmsford, Canterbury and Lancaster are much smaller than their officially designated city limits, so they have a significantly lower population. This means that it makes sense to combine them with their surrounding area to make a sensible sized administrative area, but that this would be a county rather than a city.

In fact, a much better sign of whether a settlement is worthy of being considered a city is actually whether it has been split from its county, as a unitary authority. All of the urban unitary authorities that currently exist in England have made it as cities under this plan - Blackburn, Blackpool, Bristol, Derby, Hull, Leicester, Luton, Medway (as Rochester), Milton Keynes, Nottinham, Oxford, Peterborough, Plymouth, Reading, Slough, Southend, Stoke, Swindon, Telford, Thurrock (as Basildon), Torquay (as Exeter) and York.

Aside from these, the plan designates other cities in England that weren't already unitary authorities - Burnley, Cambridge, Colchester (inc. Clacton), Crawley, Farnborough (inc. Aldershot), Gloucester (inc. Cheltenham), Guildford (inc. Woking), Harlow (inc. Bishop's Stortford), Hastings (inc. Eastbourne), Ipswich (inc. Felixtowe), Northampton, Norwich, Preston (inc. Chorley), Thanet (consisting of Margate and Ramsgate) and Wycombe (inc. Beaconsfield). Many of the cities in this list are polycentric, having more than one fairly densely populated city centre, but they have a sufficiently high population of sufficiently high density to be qualitatively different to their surrounding counties.

The differences between cities and counties are apparent when the borders are overlaid on a map of population density, similar to the one in the Final Proposal section of the previous post (this one is worth clicking on, to zoom in and see the detail):

London

Surrounding London (in the states of Surrey and Essex) are several of these cities, sometimes forming corridors around major routes into London. These are Luton, Wycombe, Slough, Reading, Farnborough, Guildford and Crawley in Surrey and Harlow, Basildon, Southend, Rochester and Thanet in Essex. If the states have adequate autonomy over urban development and planning, these cities could be permitted to expand within their borders. This would allow for London to grow within key access corridors, without giving way to uncontrolled urban sprawl.

These corridors around established population centres allow for the possibility of a "Green Wedge" approach to London's growing suburbs, rather than the current far more restrictive greenbelt. The greenbelt was originally instituted to protect natural spaces around cities, but is so restrictive that it now has a stifling effect on London and the many other cities it affects, attempting to freeze the growth of a city at a particular arbitrary point in time. By encouraging growth exclusively within these corridors, green space remains accessible and urban sprawl is curtailed, but people are still able to live near to where their skills are in demand.

One further thing to note about the cities in this proposal is the presence of some cities that have an "outer district". These are Bristol, Leicester, Edinburgh, Nottingham, Cardiff and Belfast. Whilst still too small to be metropolitan states, these cities are too large to be contained within a single administrative division. Combining the suburbs of a large city with the rural area surrounding it would again cause friction between the different needs of these two groups of people, so I carved out 6 "cities" that allow these populous suburbs and satellite towns to have their own local government.

An alternative to this would have been to simply take the large city in its entirety, then split it down the middle, giving a North and a South (or East and West) of each city. I decided against this, because as with London's central and more peripheral areas, the high population density at the centre of a city has unique requirements that are likely best served by having their own administration. To split large cities down the middle would deny the opportunity for centre and suburbs to each benefit from a more aligned government.

As an extreme example of this density discrepancy, I present to you a version of the population density map above, zoomed in on London. Even though Middlesex and Croydon have population densities higher than any of the other states outside London (2,911 and 2,821 people per square km respectively), the state of London itself has a population density over 3 times as high, at 9,115 people per square km:

Looking at the cities outside of the metropolitan states, it is clear that the 6 cities with central and outer divisions are similar to this. The central "cities" are by far the most densely populated, ranging from 4,009 to 5,553 people per square km. This is more than double the density of their respective outer cities, and most other cities under this plan.

Borders

Because I mainly based these borders on geographical features, I was able to produce a map that shows which feature was used to make the border. In the map below, motorways are shown as red, A-roads as orange, railways as purple, rivers as blue, national park/AONB borders as green, existing county borders as yellow, existing district borders as dark grey and other smaller features as light grey:

Full List of Divisions

Just in case anyone wants it, below is the full list of all 256 divisions, along with the the key statistics of each. The final two columns are a possible two-letter state code and single-letter district code that provide each district with a unique identifier. (The two-letter state codes have also been chosen to avoid any clashes with US two-letter state codes, to avoid confusion between for example; Elgin, SC and Elgin, SL or Manchester, NH and Manchester MH).

These could ultimately be used to supersede postcodes, finally aligning the postal address system with the administrative geography of the country. This would avoid confusing situations such as Barking having the postcode area IG (Ilford) rather than E (East London), or Aberystwyth having the postcode area SY (Shrewsbury) rather than a Welsh postcode area.

(And Northern Ireland. I considered the title "Federal United Kingdom", then binned that for obvious reasons. Seriously, after the whole North Macedonia thing, it should be clear that deciding what a country is called is just an absolute minefield.)

Currently, there are various levels of devolved power in the UK. There are the four main countries - England, Scotland, Wales and Northern Ireland. Devolution is applied inconsistently across these, with Scotland, Wales and Northern Ireland heavily devolved with their own legislatures (the Scottish Parliament, Northern Ireland Assembly and Senedd Cymru respectively). England does not have its own devolved parliament, and instead is governed directly by the national parliament at Westminster. This has given rise to what is known as the West Lothian question, which queries the legitimacy of a system in which a Scottish MP gets a vote in something that affects England but not Scotland, whilst an English MP does not have a reciprocal power as such matters are decided by the Scottish Parliament.

This is not the only glaring inconsistency however - each of the countries with a devolved parliament receives different devolved powers from the national government. Scotland and Northern Ireland also have separate legal systems from England, but Wales shares the same legal institutions and has only been able to set laws independently from Westminster since 2006.

Then there is London, which has a devolved executive - the Mayor and the London Assembly. This gives London a large degree of autonomy from the central government when it comes to things like infrastructure spending and strategic planning, but it misses out on many of the powers that the devolved countries are granted, and has no devolved legislature at all.

Other large cities have seen increasing devolution in recent years, for instance Greater Manchester has had a directly elected mayor since 2017. There are now several cities that have benefitted from such devolution, but again both the structure of the authority and the devolved powers they have are often inconsistent.

The UK has long been a very centralised state, which can leave certain areas to be forgotten about by the national government, being left to wither - an issue that has been written about at length, and has been noted yet again in this Economist article. Of course, all of the areas mentioned above have benefitted from varying degrees of decentralisation as a result of devolution, but:

1. There are many areas that have experienced no devolution, and so are in effect still governed with disinterest from afar.

2. The areas that have seen some devolution are treated inconsistently, leading to unnecessary complexity.

3. The devolution of power is (at least in principle) still entirely at the discretion of the central government in Westminster, and can be rescinded at any time.

As might be clear from the last few posts, I think federalism is a good way to improve the state of democracy in a large unitary country. The fact that the UK is already part-way along this road, having significant devolution to various areas, should make a transition towards federalism a welcome simplification. I will follow the guidelines from the previous post to design regions that should facilitate a federation that runs smoothly. These are:

• No state should be larger than 8 times the population of the smallest.

• All states should be between 200k and 25.6m in population, or more ideally between 800k and 6.4m.

• Where a region contains rural areas and a large contiguous city, if both are large enough in population to be separate states, they should be.

Given this preamble, if you want to skip to where I start getting to the point, click here. If all you want is the final proposal, click here instead. Otherwise, let us begin.

Where to Start

So, first things first - what if we just took the four main countries plus London (with its devolved executive) and gave them all the same powers as equal states in a federation?

Even having removed Greater London from England, it is still far too large and would be completely dominant in any federation. England is well over the 25.6 million limit discussed in the previous post, and it is almost 25 times the size of Northern Ireland.

Northern Ireland itself is fairly geographically isolated and culturally distinct, so combining it with any other areas to reduce the difference between the largest and smallest states is a complete non-starter. This gives us a hard limit on the size of the largest state that we can accept. If Northern Ireland is the smallest state, and we want no state to be more than 8 times the population of the smallest state, we are limited to a maximum state size of 14.5 million people.

Combined Authorities

Outside of London, there are several more "combined authorities" with devolved funding, powers and directly elected mayors. These are often city regions, so separating these from their rural surroundings could be an easy win. Using these to split England further gives us the following 15 entities and populations:

Despite removing these 10 combined authorities, some of which are large cities, what is left of England is still almost as big as all of the other states combined, which is unacceptable. We have also now introduced several even smaller entities - the state of England is now 41 times larger than Tees Valley.

Regions

For statistical purposes, the UK is divided into 12 "Regions" that currently have no distinct governmental powers. Many proposals of federalism in the UK have used these, so we can see what we would get if each of these were turned into a state:

These are relatively evenly sized - the South East has around 5 times the population of Northern Ireland, which is acceptable. These divisions have been around for a while though, and they have not taken off as actual administrative regions for a reason. Most of them contain a mixture of cities and rural areas that do not naturally work together.

Regions & Combined Authorities

If we now split the combined authorities from the regions, we generate 21 states:

Splitting out the large cities in this manner makes the divisions far more likely to be functional - their respective governments will be able to focus their attentions on the relevant rural or urban issues respectively. Unfortunately however, the South East now has over 12 times the population of Tees Valley. As can be seen from the map, there is also an aesthetic issue - some of the regions have holes in them. This is not necessarily an issue, but it does make them look quite untidy which could make them unpopular, and be a barrier to implementation.

This is a good start though - from this basis, we can design states for the UK. We want them to be comfortably within the size limits, moderately consistent in character (urban or rural) and reasonably natural feeling, respecting local identities.

Going Further

We can make adjustments to these 21 states to improve the proposal dramatically. For ease of reference, I will also suggest appropriate names for the proposed states that are a little less unwieldy. Most will be based on ancient kingdoms that occupied similar areas during the Heptarchy:

Kernow (Cornish for Cornwall)

Cornwall has a fairly independent streak, and although on its own it has quite a small population, Cornwall and Devon together are culturally similar and have a combined population of 1,750,000 which can be split from the rest of the South West.

Wessex (after the ancient Saxon kingdom)

West of England (Bristol & Bath) has a significantly lower population density than the other city-regions, so it could be combined with the remainder of the South West to form a state with a population of 3,540,000.

Essex (after the ancient Saxon kingdom) and Surrey (after the county of Surrey)

The "Home Counties" bordering London are quite different in character to areas further away from the capital. Essex, Hertfordshire, Buckinghamshire, Berkshire, Surrey and Kent are all part of London's commuter belt, giving them their own particular concerns and interests different to other parts of the UK.

Due to their population density, all of these counties combined would make for a very populous state, so it would make sense for there to be two such states. The difference between the Western and Eastern home counties is probably greater than the difference from North to South, as Essex and Kent both have coastlines and significant industry, while the other counties further inland have a very service heavy economy and are some of the wealthiest areas of the UK outside London.

This suggests that the counties of Essex and Kent could form one state (Essex) with a population of 3,070,000. The remaining home counties could form another state (Surrey), though excluding the districts of West Berkshire, Aylesbury Vale and Milton Keynes which are still fairly distant from London. This would give the state of Surrey a population of 3,460,000.

Sussex (after the ancient Saxon kingdom)

With the home counties removed, the Southern parts of the South East (Hampshire, the Isle of Wight, East Sussex, West Sussex and West Berkshire) can form the state of Sussex with a population of 3,240,000.

Anglia (after the ancient Angle kingdom)

Cambridge and Peterborough is a little on the small side, but with the home counties removed from the East of England region, its remnants (excluding Bedfordshire, which we will use later) can be combined with Cambridge and Peterborough to form the state of Anglia with a population of 2,720,000.

London, Middlesex and Croydon

London is often split into Inner and Outer London for statutory and statistical purposes. Outer London is further divided by the river Thames, with areas to the north of the Thames being quite different in character from the south due to greater tube network coverage, greater population density and having required much greater reconstruction following the second world war. Inner London (as defined by the ONS for statistical purposes) has a population of 3,230,000 and should probably continue to be referred to as London. North Outer London (North London as defined by the Boundary Commission, excluding areas of Inner London) has a population of 3,150,000 and overlaps significantly with the old county of Middlesex. South Outer London has a population of 1,790,000 and the largest city it contains is Croydon. Splitting London into 3 parts should not stop them coordinating on large projects such as the Oyster network.

Bromwich (from Beorma)

Beorma is the root of Birmingham, West Bromwich and Bromsgrove. Bromwich therefore seems like an appropriate name for the state made from the combined authority of the West Midlands (Birmingham).

Mercia (after the ancient Angle kingdom)

The rest of the West Midlands has a large hole cut out of it for Bromwich, Splitting Shropshire and Staffordshire on the top from Herefordshire, Worcestershire and Warwickshire on the bottom. There are better things we can do with the bottom 3, so it makes sense to remove them from Mercia, but this leaves quite a small state. Cheshire in the North West is separated from the rest of the North West by Liverpool and Manchester, so this can be added to Mercia instead. The M1 forms a natural dividing line close to the border between Derbyshire and Nottinghamshire, so we can move Derbyshire from the East Midlands to Mercia as well, giving a population of 3,530,000.

Cymru (Welsh for Wales)

Herefordshire shares a border with Wales and is much more sparsely populated than any of the English counties that it borders (it is actually one of the least densely populated counties in England). In this respect it likely has more governmental requirements in common with Wales than with other counties in the midlands. In fact, the prevalence of farming in Herefordshire, along with significant Welsh cultural presence in the western parts of the county have led to previous proposals to shift the Welsh border to include Herefordshire. Following through with this would make a lot of sense and only increases the population of Cymru to 3,260,000.

Hwicce (after the ancient Saxon kingdom)

In between the states so far defined, we have a number of counties that we have not done anything with. Worcestershire, Warwickshire, Oxfordshire, Bedfordshire and the districts of Aylesbury Vale and Milton Keynes can be combined into a state in the centre of England. Adding Northamptonshire too, from the East Midlands brings its population to 3,700,000.

This English heartland sits on the border between the North and the South, and is sandwiched between London and Birmingham making it extremely well connected and an attractive hub for many logistics firms. This region also contains the majority of the so called "Brain Belt", including Oxford, Bicester, Milton Keynes and Bedford, which along with Warwick have an unusually high density of headquarters for international and high-tech firms.

Far from being a contrived amalgamation of disparate areas, this state is fairly internally consistent, and would be the third wealthiest state per capita after London and Surrey. The ancient kingdom of the Hwicce was made up in large parts from the Cotswolds, Worcestershire and Warwickshire, but there is evidence for its influence reaching as far east as Northamptonshire and Rutland, making it an apt namesake.

Lindsey (after the ancient Angle kingdom)

Having lost Derbyshire and Northamptonshire, the East Midlands can reclaim the unitary authorities of North Lincolnshire and North East Lincolnshire from their bizarre inclusion within Yorkshire and the Humber. This gives Lindsey a population of 3,060,000.

Elmet (after the ancient Celtic kingdom)

Sheffield would be a relatively small state. Although Sheffield and Leeds both have their own combined authorities, they are only 35 miles apart, and are effectively joined into a single metropolitan area by the cities of Barnsley and Wakefield. By combining West Yorkshire with the Sheffield City Region, we can create a larger metropolitan region covering much of South West Yorkshire with a population of 3,700,000.

Northumbria (after the ancient Angle kingdom)

North of Tyne only incorporates the northern half of the "Tyne and Wear Metropolitan County" (a fairly large conurbation including Sunderland), but it also includes Northumberland which is very rural. Combining the Tyne and Wear Metropolitan County with Tees Valley gives us a metropolitan region with a population of 1,830,000. This region is split in two by County Durham, but we can deal with this later. The remainder of the North East region plus Northumberland have a population of only 766,000 which could be combined with the remaining Yorkshire and the Humber region.

Deira (after the ancient Angle kingdom)

After losing North Lincolnshire, North East Lincolnshire and Leeds, the Yorkshire and the Humber region can absorb what is left of the North East region from above, giving a state that is very large geographically, but very rural, with a population of 2,350,000. This state would contain only two moderately sized cities (York and Hull), but would contain three large National Parks (North York Moors NP, Yorkshire Dales NP and Northumberland NP) and four Areas of Outstanding Natural Beauty (Northumberland Coast AONB, North Pennines AONB, Nidderdale AONB and Howardian Hills AONB).

Rheged (after the ancient Celtic kingdom), Merseyside and Manchester

With the North West already excluding Liverpool and Manchester, and having moved Cheshire into Mercia, it is left with a population of 1,710,000. Greater Manchester can be left unchanged and the city-region of Liverpool (Merseyside) can incorporate the fairly urban unitary authority of Warrington.

Glesga (Scots for Glasgow) and Scotland

Glasgow is a very large urban area within the largely rural Scotland. Splitting it into its own state would make governing much more straightforward, and would not stop Scottish and Glaswegian governments from working together on projects if they felt so inclined. Specifically, taking the combined councils of West Dunbartonshire, East Dunbartonshire, North Lanarkshire, Inverclyde, Renfrewshire, East Renfrewshire and Glasgow City as a separate state from the rest of Scotland would result in a metropolitan state of 1,550,000 people and a largely rural state of 3,750,000.

Ulaidh (Gaelic for Ulster)

As before, no changes need to be made to Northern Ireland. A more interesting name wouldn't hurt though.

Proposal Based on Existing District Borders

This gives us the following 23 states:

These 23 divisions would probably suffice - the largest (Scotland) is now less than 2.5 times the size of the smallest (Glesga), and they might generate more enthusiasm for becoming federal states due to having greater internal similarities than the current statistical regions.

• The densely populated metropolitan states of London, Middlesex, Croydon, Bromwich, Manchester, Merseyside, Elmet, Northumbria and Glesga have autonomy to manage their affairs free from the demands of more rural constituents

• The commuter belt states of Essex and Surrey can easily collaborate with the three states making up Greater London on issues such as transport links and the greenbelt.

• The semi-rural states of Wessex, Hwicce, Sussex, Anglia, Mercia, Lindsey and Rheged have a lower population density than the commuter belt, but are still dotted with bustling towns and small cities.

• The very rural states of Kernow, Cymru, Ulaidh, Deira and Scotland each have their own particular cultures and requirements, which make them cohesive states despite their remoteness.

Making Use of Existing Features

By relying on existing county and district borders, we have exhausted the low hanging fruit, but we can still do slightly better. There are a few more issues that it would be good to address, that will be possible if we allow ourselves to use roads, railways, rivers and National Parks/AONBs as borders as well.

The map below shows the National Parks, AONBs and National Scenic Areas (Scotland) overlaid upon the proposal based on district borders:

We can pick through the proposal above and make finer adjustments to try to resolve issues and make the states as cohesive as possible:

1. Northumbria is split into two by the very sparsely populated County Durham in Deira. Rather than moving the whole of County Durham into Northumbria, we can simply include the city of Durham itself, and anything East of it. This joins the two parts of Northumbria together whilst maintaining the high population density of a metropolitan state.

2. There are several large, very densely populated cities on the south coast (Bournemouth, Southampton, Portsmouth and Brighton) that are likely to have very different focuses from the surrounding rural counties that make up the rest of our state of Sussex. We can split these off, along with the Isle of Wight into a new metropolitan state. I will name this Solent after the strait of water between the South coast of England and the Isle of Wight. This is actually not a completely new idea, and a "Southern Powerhouse"/"Solent City" has been mooted before (though not without controversy).

3. The fringes of Glesga turn very quickly into very rural Scotland (West Dunbartonshire actually includes some of the Loch Lomond and the Trossachs National Park). Trimming some of this off, allowing the rural areas to be governed by Scotland would be sensible, whilst the densely populated North of South Lanarkshire (Rutherglen, Cambuslang, East Kilbride and Hamilton) are within the metropolitan area of Glasgow, so should be included.

4. The Western edges of the Yorkshire Dales National Park and the North Pennines AONB are in Rheged. By shifting the border between Deira and Rheged to the river Eden, this is avoided.

5. Kernow is significantly less densely populated than Wessex, but most of Exmoor National Park is in Somerset rather than Devon. National Parks and AONBs tend to have few residents, so it would be appropriate to move the rest of Exmoor NP, the Blackdown Hills AONB and all of the Quantock Hills AONB into Kernow.

6. With Herefordshire now being part of Cymru, the small sliver of Gloucestershire that is West of the river Severn is on the wrong side of a very natural border. Moving this area to Cymru removes another very sparsely populated area from Wessex. This area includes the Wye Valley AONB which currently straddles the border with Wales.

7. The counties of Essex and Kent are both quite large, extending a long way from London, which makes the Northern reaches of the county of Essex as well as High Weald AONB in Kent quite different in character from their more London focused parts. These areas could be ceded to Anglia and Sussex respectively, to better match their composition.

8. The North Wessex Downs AONB covers most of West Berkshire, but extends beyond it in most directions. Now that the densely populated Solent has been removed from Sussex, it is a much more rural state than the others surrounding it, making it sensible for the entirety of this AONB to be included within it. This being said, the name of the AONB might need to be changed, due to it being in the state of Sussex rather than Wessex. "The Berkshire Downs" would probably suffice. Notably, combined with the change above, Sussex now contains all of the North Wessex Downs AONB, the High Weald AONB and the South Downs National Park, which means that an even higher percentage of its land is covered by conservation areas than Deira.

9. Bromwich is surrounded by a few towns that might benefit from being served by the same government as the metropolis itself. Bromsgrove, Redditch, Nuneaton and Tamworth could all be considered commuter towns of the Birmingham conurbation. Also, by including Nuneaton we remove the hook that protrudes from the North of Hwicce.

10. Greater London is surrounded by the natural border of the M25, while the North and South circulars (the A406 and the A205) serve as a very natural border for inner London.

11. Other borders can be tidied up a little, following rivers, railways or roads where they are fairly close to the existing county border.

(As a side note, if we are using roads as borders, it is worth putting the border such that the road itself is clearly inside one or other of the states. If jurisdiction and responsibility over the road is not clear, it may not be maintained, and could be a source of conflict between the states. This is an implementation detail, and therefore not something represented in the maps below, but it is important to consider in any proposal changing border lines.)

This gives us the following map showing the starting point using existing county and district boundaries, the areas that are to change hands, coloured in various shades depending on which state they are going to be a part of, and the final proposal:

Final Proposal

Importing the data into Google Maps allows me to show a zoomable map of these states.

The final 24 states have the populations, areas and population densities as shown below, this time ordered by density:

You can see that the largest state (still Scotland) now has just over twice the population of the smallest (Sussex), so there should be no California/Wyoming problems here. Half of the states (12) are varying degrees of rural, with population densities below 300 people per square kilometer. Around half the population (31 million people) live in these states, which gives a good balance between urban and rural.

The state of London has a population density more than three times that of the next most dense region, justifying it being its own state, as it is likely to have unique requirements even when compared with other metropolitan states. The other 9 metropolitan states have a population density over 1000 people per square kilometer - more than any US state, and higher than Harris County, Texas (Houston) or Los Angeles County, California. Finally, Surrey and Essex bridge the gap between metropolitan states and rural states, being a mixture of urban and rural in the commuter belt of Greater London.

You can see the population densities of the different states if we draw these proposed borders onto a map showing the population density of each census tract. In the map below, the yellow shaded areas have a population density below 10 people per square kilometer, the red shaded areas have over 1000 people per square kilometer, and the various degrees of orange are in between:

Is 24 too many states? After all, the "Regions" proposal only created 12. Personally, I don't think so - the smallest covers just over 1.6 million people - in between the sizes of the US states of Hawaii and Idaho, and almost 3 times the population of Wyoming. This is clearly a functional size, and this number of states allows them to have their own individual characters, without feeling like they are a random jumble of dissimilar areas. Many federal countries have a comparable number, or even more states than this:

It is also worth noting that by changing the borders away from the existing county and district borders, I have broken local government. It is generally accepted that local administrative units should be directly subordinate to states, and therefore should not cross state lines. There is therefore some work to do in adjusting the counties and unitary authorities that make up the UK to be compatible with this proposal. Don't worry - this post is already more than long enough, so all those maps can be saved until the next post.

There are many countries around the world that use Federalism as a system of government, and some work better than others.  It would be good to improve the standard of democracy around the world, and so if any countries were considering becoming federal, it would be good to know what features get the best results.  Given an existing federation, any changes will necessarily take a significant amount of time and effort to make, so again, knowing what features get the best results would be very useful in determining what changes to focus on.

Ideally, it would be good to realise all of the benefits listed in the previous two posts - legibility, antifragility, greater freedom, political incubation, a distributed economy, closer proximity to the government and less conflict.  What we need is to isolate any factors that get in the way of these benefits, so that existing federations can pursue reforms, and unitary countries can avoid predictable future issues.

So if our aim is to have a well-functioning federation, what do we need to think about regarding the states?

Composition

As is demonstrated in many existing federations - wherever different cultural groups reside in different areas, it is clearly worthwhile to allow them a certain autonomy in their laws and governance.  This reduces both the likelihood of oppression, and people’s perception that they are being ruled over by disinterested outsiders.  In the modern era however, there is another division that is worth considering.

Rural areas and metropolitan areas have very different requirements, focuses and cultures.  It makes sense for significantly different areas to have different rules, and to be independent from each other, as otherwise there will always be a power struggle between the different demographics.  Whether it is a case of legislators ignoring rural poverty while they focus on an exciting development in a burgeoning city, or a case of subsidising farmland while neglecting inner city degradation, it is very difficult to represent such different groups simultaneously.  This is actually already an issue in the European Parliament where 6 MEPs represent the entirety of Yorkshire and the Humber. The needs of a village in the North York Moors, and the needs of people in inner city Sheffield are very different, and require very different solutions and expertise. A small selection of obvious conflicts are in the table below:

A reasonable aim would therefore be for states to be either urban or rural, rather than both.  Avoiding states that contain both a very large city and a significant number of rural residents will avoid many of these tensions.  The question then becomes where to draw the line - what about a state containing a few small cities and a large rural population?

Due to the way that cities scale, a city of 1 million residents will have far more than double the number of high density inner city residences than a city of 500,000.  This suggests that the kind of environments that make cities so different to the countryside are likely to grow superlinearly with the size of the city.  Although some tensions are inevitable, this implies that the same number of people that might reside in a large city, but broken up into a number of small cities and towns, could be rolled into largely rural states with much less of a problem.  Another mitigating effect of multiple cities and towns is that they would likely be more spread out across the state than a single conurbation, making more of the rural population near to a town or city, reducing the cultural gap further.  Whilst it depends heavily on the size of state that is being sought, a reasonable rule of thumb would be that once a city is large enough to form its own state, it should probably be carved out to avoid these conflicts.  This would mean that people in the countryside in the vicinity of a major conurbation would not find themselves hugely outvoted by the city dwellers.

This goes against the current make-up of US states, many of which are a mixture of large cities and very rural areas.  No US states have a population density over 1000 people per square kilometre - although there are several very rural states with no large cities, there are no states with large cities that do not have substantial rural populations as well.  In states such as New York, California and Illinois, the rural population is smaller than the urban population, resulting in their wishes and concerns often being ignored, whilst in states such as Texas and Georgia, despite the huge cities of Houston, Dallas and Atlanta, the rural population is larger than the urban population, resulting in the urban population's wishes and concerns being ignored instead.

There are two different justifications for this set-up that are often given - the US's voting system and the ability for a state to be independently self-sustaining, but these are not particularly compelling reasons:

In the US voting system the senate and presidency are heavily influenced by state borders - the senate gets 2 senators per state, each elected on a first past the post basis, so that even a large minority within a state may get no representation in the senate.  The Electoral College system of voting for the presidency works on a similar, “winner gets all” basis within most states.  This means that the rural minority in California, and the urban minority in Texas effectively get no say in the senate or presidency.  In theory, in a state split very close to 50/50, this could be fair, as a small shift in appeal one way or another would swing the state, however most states are not like this, and even if a state was, it may not last due to population migrations towards or away from cities.

Due to the particular voting systems used, suggestions of having urban states in the US runs into accusations of “gerrymandering state borders”, however this is not a problem if the voting system used does not depend on these borders.  Although the voting system will be difficult to change in the US, there is no reason why any other country must replicate their system.  A nationwide election i.e. the presidency, could be done on the total national vote of a country, with no distinction between voters from different states.  An election of representatives meanwhile, i.e. the senate, could be done using one of many systems of proportional representation.  Therefore, on a national level the state borders don’t need to affect anything politically, but on a state level, internal similarities can reduce governmental tension and deadlock.

Regarding the other justification, of the need for states to be independently self-sustaining, there are good arguments for a country itself to have this ability.  By being self-sustaining, a country's fragility to external events such as food or energy shortage and war is reduced.  Within a country however, this argument is less persuasive - states are able to work together, and the federal government should facilitate this.

Unless a state is entirely surrounded by a single other state, with no coastline, it has options of which other states it wants to work together with.  Obviously such a situation is worth avoiding when setting up states within a federal system, just in case, but even then, the role of the federal government should mitigate this.  Even at a national level, places like Singapore and Hong Kong have been extremely successful whilst having little rural land, having to rely on trade to source the basics of survival.  Although this is quite a fragile situation for a country, it is clearly not necessarily detrimental, and this risk should be much reduced for a state within a federation.

Population Size

Too much variation in the size of different states makes federal governance difficult.  Either large states get disproportionate sway, or small states are overrepresented.  Attempts can be made to find a balance between these effects in such a way that they cancel each other out, but this is very difficult.  In the complex real world of politics, this often just means that both issues exist simultaneously in different areas.

The state of California makes up about an eighth of the population of the US and about a sixth of its economy, making its state government hugely and disproportionately influential both culturally and economically.  In the senate however, their 39 million residents have the same two senators as Wyoming’s 580,000.  For the House of Representatives, an attempt is made to distribute representatives fairly evenly by population, using a method that CGP Grey explains very thoroughly in this video, but this is only one of many spheres of influence that the state has, and even this method of representation is not conclusively fair.

Note that I am not claiming that California is systematically overpowered or systematically underpowered. Depending on the area in question it may be one or the other, but to such a significant extent that regardless of how well you try to balance these opposing effects, there will be people whose voices remain unheard in the realm that they care about.

Similarly, within the EU, Germany makes up just under a fifth of the population of the EU and just over a fifth of its economy - an even more outsized influence.  Within the EU, many countries and citizens feel that Germany sets the direction of the EU to far too great an extent, due to its economic clout. On the flip side, in the European Parliament, the smallest member state of Malta gets 6 members out of the total of 705, or slightly under 1%, despite having just over one thousandth of the EU population.

Clearly, attempts have been made to make these systems fair, but such wildly different sizes of states makes this effectively impossible.  Far better, would be to limit the sizes of states to be within a certain range of population.  This raises the question, what is the best size for a state to be, and how wide should this range be?

Upper Estimate

Let’s start with finding an upper estimate for the target size of states - the largest population that can be dealt with as a single state before significant issues start cropping up.  The more populous a state is, the more difficult and complex it is to administer.  This complexity introduces fragility to the state itself, but a large state can also reduce the antifragility of the country as a whole, as there are fewer states, which means fewer entities trying different strategies.  Another issue with large states is again that of representation - it is harder for politicians to be in touch with the people, so it feels less democratic.  This suggests that a good approach for placing an approximate upper bound on the size a state can be whilst being well run, is finding how well it can perform the job of politically representing its populace.

In order to do this, firstly we need to know the maximum number of people per representative - the largest number of people that a single person can effectively represent. How to find this is not obvious, but we can work through two possible metrics for determining this.  These are very rough - effectively Fermi estimates, but that should give us somewhere to start:

1. Whilst arguably not essential, it would be good for a representative to be able to address all of their constituents in person.  This would mean being able to host all of their constituents in a location to give a speech or rally.  A large stadium is not strictly necessary for this, but more people than would fit into a large stadium would be difficult to host in an alternative location.  A large stadium tends to have a capacity of between 40,000 and 90,000 people, so one estimate for the maximum number of people per representative can be between 10,000 and 100,000 people.

2. Similarly whilst they might not actually do this, it would be good for a representative to be able to meet all of their constituents in a given year.  There are about 1,700 working hours per year, and if you spent every minute of this meeting a different person, that would allow you to meet 102,000 people. This is a bit extreme, as even the most in-touch representative would be unlikely to spend more than half of their time doing this, and 5 minutes is really the bare minimum to actually have a constructive, informative conversation with someone.  These assumptions reduce it down to 10,200 people, so we are again left with a maximum number of people per representative of between 10,000 and 100,000 people.

We can compare this with how real countries represent their populaces.  India has 790 representatives across both parts of their bicameral legislature.  With a population of 1.24 billion, this means that there is 1 representative per 1.56 million people.  On the other end of the spectrum is Nauru, whose 19 member parliament represents their 9,500 strong population, giving 500 people per representative.  Looking across all of the 200 or so countries in the world, it can be seen that the median and mean of people per representative are 36,000 and 72,000 respectively.  These values are reassuringly within the estimates that we found above.

The next thing we need is to estimate how large a parliament/state legislature can be before it becomes dysfunctional.  For this, we can use Dunbar’s number, which is a theoretical upper limit on the number of people with whom one can maintain stable social relationships.  This is a reasonable number to use, as it is useful for representatives to be able to know and interact with every other representative, in order to successfully navigate the process of drafting legislation.

Dunbar’s number is estimated to be between 100 and 290, with the most common estimates being around 150.  Again, real legislatures range from 741 representatives for the EU parliament to 14 representatives for the small island nation of St Kitts & Nevis.  The median and mean of legislature sizes are 120 and 180 respectively. We can use these numbers to give us a range of estimates for where the upper estimate of the ideal size of a state might be.

• 10,000 people per representative times 100 representatives gives us 1,000,000 people - not so much an upper estimate, but a fairly reasonable number of people in a state.

• 100,000 people per representative times 290 representatives gives us 29,000,000 people - an upper bound that pushes all of the considerations above to their limits.  Germany and California are both well above this, but if we are looking to suggest a kind of “best practice” for the size of states, it might do to be a little more conservative.

• Taking the geometric mean of both 10,000 with 100,000 and 100 with 290, we get 32,000 people per representative and 170 representatives.  This gives us 5,440,000 people in a state - comparable with Slovakia or South Carolina.

Taking further inspiration from existing countries, we can review which countries are particularly well run.  Large entities are more complex, and therefore more difficult to run, so although a small country or state can still be run badly, a large country or state is less likely to be run well. We can reasonably expect to see a range of sizes of entities being run poorly, but only relatively small entities being run well.

The Democracy Index consists of 5 components that measure aspects of democracy.  These aspects range from the electoral process itself to the political culture. All of them are important, but the one most relevant to finding the ideal size of state for a government to function well is unsurprisingly called “Functioning of Government”. Looking at the top scoring countries by this metric can give us further insight into what sizes of country or state allow for a well run government.  For this, I will split federal countries into their component states, as this is the entity that we want to judge.

The top scoring countries for Functioning of Government, all scoring 9.64/10 are:

The next group scoring 9.29 are:

Remaining countries scoring >8.5 are:

In the group of countries scoring >8, we finally get a large non-federal country.  This is Japan, with a population of 127m.  Despite not being federal however, in Japan 70% of government expenditure is administered locally, which is more than many federal countries. This means that although the central government has the power to take back control of this expenditure (a power it might not have in a federal country), it is reasonable to treat Japan's provinces as states for the purposes of comparing how well the government functions:

Finally when the score drops below 8, we encounter entities that have populations over 25 million.  There are many small entities too, as expected, but we now start to see large countries that are generally considered successful, despite frequent complaints about poor governance.

Although it is not particularly statistically rigorous and there are many other variables that confound the data, we can at least observe that all countries with Functioning of Government score greater than 8 consist of entities that have a population less than 25 million.  With these 20 high scoring countries, if we split the federal (or functionally federal) countries into their constituent states, we get a list of 127 entities (113 states and 14 unitary countries).  As already noted, the largest of these is Taiwan with a population of 24 million, whilst the smallest is the canton of Switzerland called Appenzell Innerrhoden with a population of 16,000.  Unsurprisingly, a large number of these entities are really quite small, so the median size of these 127 entities is 1.4 million, whilst three quarters of them are smaller than 4 million.

The largest gives us a similar number to before for an upper bound, but we are still looking for a sensible statistic to inform a more modest recommendtion for how populous an ideal state might be able to be.  Whilst larger than the median, the mean of this selection is still quite small at 3.1 million, due to the large number of very small entities. We can instead use the RMS, which weights larger entities more, as they have more people in them. The RMS of the population of these entities is 5.2 million.

We now have a couple of different estimates for upper limits on how populous we might want states to be in an ideal world, so we can turn our attention to the other end of the scale.

Lower Estimate

Small states have their own problems that are very different to those of large states. There is a higher administrative overhead for small states, as governments have certain relatively fixed costs that do not vary significantly as the size of the state changes. This is very similar to the pressure on companies to grow and merge in order to find economies of scale. In the extremes, very small states can be too small to run their own services effectively, needing to pool resources with other states or get federal help. There is also a greater risk of regulatory capture, as a smaller government is generally more easily bought or influenced than a larger one. These issues suggest that an approximate lower bound for state size might be found by investigating the necessary economies of scale in government functions.

An obvious place to start, where economies of scale are very important is healthcare. For this rough estimate, I will use UK figures and terminology, as it is what I am familiar with and the UK has a fairly functional health system, so it shouldn’t be too far off.

When splitting a country into states, it would be sensible if each state had a large enough population to warrant a hospital with a Major Trauma Centre (one with operating theatres and the necessary equipment to deal with emergencies and serious trauma cases). The smallest Major Trauma Centre in the UK is in Newcastle with 620 beds (most have between 800 and 1200 beds), but in order to get people to hospital quickly, governments would usually aim to have more coverage across an area than a single hospital, so you would generally see multiple smaller hospitals and at least one large one in any particular region. To comfortably meet this, it would be sensible to aim for a large enough population to support a minimum of double this (1,240 beds at a bare minimum, or more conservatively around 2,000 beds).

Across the OECD, the number of hospital beds per 1,000 people ranges from 1.5 to 13 with the median around 4. Taking the German figure of 8 beds per 1,000 people, we would need a population of 155,000 to warrant the provision of 1,240 beds.  With only 2 beds per 1,000 people, if we targeted 2,000 beds we would need a population of 1,000,000.

Alternatively, we can look at policing. Avoiding corruption is important, so as a bare minimum, you need some form of “internal affairs” that can police the police.  Of course, this could be done at a federal level, but a state having its own (effective) internal affairs department is beneficial for its autonomy. Having more than 5% of police being internal affairs would be egregiously inefficient, so we can use 5% as a rough estimate. At the same time, we can use Dunbar’s number again - in order to avoid corruption within internal affairs, it would be good to have enough people that everyone can’t know everyone else. This implies that we want at least Dunbar’s number of police officers in a state’s internal affairs department.

The number of police officers per 100,000 population varies between countries - Canada, Sweden, Switzerland, England, Australia and the US have around 200 police officers per 100,000, Belgium, France and Germany have around 350, but Uruguay, Spain and Russia have 500-600. With these numbers, we can again produce a range of estimates for how few people could live in a state before particular problems might start to arise:

• If we assume Dunbar’s number is 100, we would need 2000 police to give us 100 internal affairs officers if they made up 5% of the force.  If we had 600 police per 100,000 people, we would then need a population of 330,000 to justify the requisite number of police.

• Taking the other extreme, we can assume Dunbar’s number is 290, and that we need only 200 police per 100,000 people.  This means we would need 5,800 police officers, which would require a population of 2.9 million.

• In the middle, if we again assume Dunbar’s number is 170, and that we need 350 police per 100,000 people, we need 3,400 police officers, requiring a population of 0.97 million.

Sensible Size Range

These estimates are just that - estimates. There is nothing fundamental stopping a smaller or a larger population from being governed well. It is evidently possible for large, highly centralised states with over 50 million people to do quite well and be considered democratic, as evidenced by France and South Korea, whilst a small state of 50,000 people could have a Major Trauma Centre if it wanted, regardless of cost or efficiency concerns. Furthermore, just as states could rely on federal police to operate an internal affairs unit, states could pool their resources and open a major hospital jointly. The objective here is simply to make it easier. By reducing the number of hurdles to overcome for a government to be effective and democratic, it becomes more likely that any given government will achieve this. These numbers therefore help to give us some bounds on the question of what a sensible size is for a state:

• Political representation gives us a “best practice” upper estimate of 5.44 million, and an upper bound of 29 million.

• Existing well run countries and states give us a median of 1.4 million, an indicative size of 5.2 million and an upper bound in the region of 25 million.

• Healthcare gives us a “best practice” lower estimate of 1 million, and a lower bound of 155,000.

• Policing tells us that 2.9 million is probably a very reasonable size, gives us a “best practice” lower estimate of 0.97 million and a more aggressive lower estimate of 330,000.

With these, we can round the numbers a bit, to produce a fairly reasonable rule of thumb.  In an ideal world, to stand the best chance at avoiding the problems mentioned above, states should range in size from a population of 800,000 to a population of 6.4 million.  This would also then mean that no state was more than 8 times the size of any other, which would make political representation much easier to keep fair, as well as keeping the differences in economic clout much more manageable.

Of course, this range might not suit every country, so a wider range is also possible to produce.  A quarter of the bottom of the range, and four times the top of the range gives us 200,000 and 25.6 million - both in line with the more extreme numbers above.  It would not be sufficient to have states ranging in size from 200,000 to 25.6 million however, as this would allow the largest to be as much as 128 times the size of the smallest. Better would be to limit states within a country to a smaller range within this, in which no state can be more than 8 times the size of the smallest.

Why 8 times? You may ask. Keeping states' populations within a factor of 2 of each other would surely be even better... The issue is one of practicality. Splitting a country into divisions that seem relatively natural is essential for giving its constituent states a feeling of legitimacy. Often pre-existing political borders make up the borders of a state, or natural features such as rivers or mountains form natural dividing lines. By forcing states into too small of a size range, you lose flexibility to draw borders in appropriate places, and risk people feeling that they were arbitrary or artificial, leading to lower public engagement with the state institutions.

Another practical consideration is that populations can change significantly over time. As an example, between 1850 and 1950 the population of the Borough of Birmingham in the UK went from 200,000 to 1 million - a five-fold increase in 100 years. With an acceptable population range that was too small, any rapid demographic shift would give rise to significant bureaucracy and political wrangling on a regular basis, as states had to be split or merged multiple times per century.

Ultimately, there is no concrete reason why the number should be exactly 8. It happens to be the approximate difference in size between the upper and lower "best practice" estimates above, and it is a nice round number. It allows a state at the bottom end of the range to double in size three times before hitting the top end of the range. Alternatively, a state with a population at the geometric mid-point could halve or double in size, and still have wiggle room for further population variation before running up against the limits. This flexibility seems beneficial, whilst a much wider range starts to raise questions again of how to ensure fairness between states of vastly differing sizes.

This proposal would mean that countries could choose any of these ranges of population, when setting the upper and lower limits on state populations:

Given that population is not the only relevant dimension to consider here, the fact that this process leads us to a range of recommendations, rather than just a single one is quite useful. A country that is very sparsely populated might choose to use smaller state populations, to keep the physical dimensions of states more manageable, or a more densely populated country might choose the range of larger state populations to avoid having to divide cities up into too many parts. Canada for example currently has several territories that are very large geographically, but that have a tiny population. To achieve a population of 200,000 would require Yukon, Northwest Territories, Nunavut, Nord-du-Quebec, Labrador, and Divisions 22 and 23 of Manitoba combined. India by contrast has a current population of 1.35 billion people, so even splitting it into the minimum number of states, each with a population very near 25.6 million, they would have 53 states.

Of federal countries that currently exist, only Nigeria and Austria have a range of state sizes that actually satisfy this. Nigeria’s smallest top level administrative unit is the Federal Capital (population 1.4 million) and its largest is Kano (population 9.4 million) - 6.7 times the size. Austria’s smallest state is Burgenland (population 290,000) and its largest is Vienna (population 1.9 million) - 6.6 times the size.

Mexico, Japan, Malaysia and Germany are all close-ish, with their largest states being 22.5 times, 23.6 times, 24 times and 26.4 times the size of their smallest states respectively. This sounds a long way off, but often there are outliers at both ends of the scale. In Germany the largest state of North Rhine-Westphalia has over 26 times the population of the smallest state of Bremen, but the second largest state of Bavaria actually only has just over 8 times the population of the third smallest state of Mecklenburg-Vorpommern.

German States with their Populations
Colours represent population density by census area (darker is more dense)

This is all a far cry from the US, where California has over 67 times the population of Wyoming, the EU, where Germany has over 174 times the population of Malta, or India, where Uttar Pradesh has 327 times the population of the state of Sikkim. In fact, if you count India’s territories too (districts that are directly administered by the federal government), it is even worse - Uttar Pradesh has 3125 times the population of Lakshadweep. The territory of Lakshadweep still has a representative in the lower house (Lok Sabha) which when compared with Uttar Pradesh’s 80 representatives makes their votes 39 times as powerful.

Subsequent Border Changes

All of these ideas around composition and size of states are all very well, but part of the point of federal systems is that the central government cannot unilaterally make changes like that. Because the goal here is a federal (rather than simply devolved) system of government, there must be a well defined process, and an element of consent on behalf of the state. This means that If there is a target size for states, a concrete plan is needed in advance for what happens when populations change over time. In an existing federation, this process would need to be added to the constitution or equivalent, which could be politically difficult or take time, however for a country considering becoming federal, this would simply be one of the many considerations that would need to be made during that process.

My proposal for a process that tries to maximise the autonomy of states, whilst still ensuring that the federal government can keep states to within the given size range is as follows, and would kick in when any state’s population shrinks to 1.5x the minimum or grows to 0.75x the maximum population size.

For states over 0.75x the maximum:

1. The state can propose a border line/division. This doesn't necessarily have to be a division that splits the state in two - to be valid, a plan just has to create states that are between 2x the minimum and 0.5x the maximum.  This is to avoid the successor states having to undergo this process again too soon. For example, if the country’s target size for states is 800,000 - 6,400,000 (differing by a maximum of a factor of 8), this process would trigger when the population of a state went over 4,800,000, and a valid proposal would suggest successor states ranging from 1,600,000 and 3,200,000 people.

2. The State's plan would then be put to a plebiscite, and would need to be approved by a majority in each newly proposed state. If the plan involved border changes with another state, this plan would also need to be approved by that state and any sub-regions that were changing hands.

3. If this succeeds one of two things can happen:

   1. If the federal government agrees with the proposal, it can be implemented immediately.

   2. If the federal government disagrees, new border proposals can be made, either by the state or the federal government. At this point though, whilst the federal government can make proposals, it cannot implement them unilaterally - it is up to the state to accept a proposal and put it to the vote. If any proposal receives the approval of both the affected populace and the federal government, it can be implemented immediately.

4. If nothing is able to be implemented, this process can continue until the state’s population tips over the maximum. Once this happens, one of two things can happen:

   1. If a plan has passed the plebiscite, it will be implemented immediately, regardless of the federal government’s objections. If multiple plans were voted on and approved, whichever of the plans is the state’s preferred option can be implemented.

   2. If no plans passed the plebiscite, the federal government’s preferred plan will be implemented immediately.

For states under 1.5x the minimum, a similar process can apply, but state will need to negotiate with other states for merging/splitting:

1. If all affected states agree and a plebiscite passes in all current and newly proposed states, similarly either the federal government can agree immediately, or it will automatically happen when the population tips under the minimum.

2. If the plebiscite does not pass or states cannot reach an agreement, the federal government can again make its own proposal, however its proposal may not subtract territory from states that have a population over 1.5x the minimum.  Because this proposal will be the default plan if nothing passes the vote, it cannot adversely affect any other states - it can only add territory to them.

At any other time, states should also be able to propose adjustment of their borders, with the agreement of other states affected.  If these changes get the same approval from their populace and from the federal government, they can occur. If these twin approvals are not achieved though, changes should not occur to any state’s borders unless its population has tipped above or below the limits, or it is a state gaining or ceding territory to another state in a chain of territory exchanges that directly involves a state whose population is outside the limits.

This can all be visualised as a flowchart (using the 800k-6.4m range as an example):

This effect of all of this should be to give states an incentive to think ahead, and get their population's buy in to any boundary changes. It should generally result in the populations of states remaining within the desired bounds without infringing significantly on their autonomy, but enables the country to avoid permanent deadlock if the state is dysfunctional.

Subdivisions & Consistency

Because of the autonomy that states enjoy within a federal system, there is nothing stopping a small region within a state from being semi-autonomous with respect to the state itself.  This means that if an area has a particularly unique character, but is too small to be viable as a state, the state containing it could simply grant it greater autonomy than it otherwise might have. This avoids the federal government having to interact directly with such a small entity, whilst still allowing very small populations to have a reasonable level of freedom and independence.

Some good examples of where this would be appropriate are places like Nunavut in Canada, the Shetland and Orkney Islands in the UK or Lakshadweep in India. As remote regions with low populations, they will not come anywhere close to the minimum populations given above. At the same time though, their remoteness means that wherever the state government is situated, it will still run into issues of proximity, with politicians struggling to remain in touch with the populace. The remoteness will also give these populations unique concerns that risk being overlooked by the state government if the population is an insignificant portion of a larger state.

Canadian Provinces and Territories with their Populations
Colours represent population density by census area (darker is more dense)

For such (admittedly rare) occurrences, something akin to a federation of districts within a state would be appropriate, ensuring that regardless of the state’s politics, these remote places and populations have sufficient autonomy. This then avoids the inefficiency of the national government having to deal directly with the governments of tiny populations and keeps the number of types of domestic entity that the federal government has to deal with to a minimum.

The direct administration of Washington D.C. by the US government, or the different status of Canadian territories compared with provinces are all areas where people have to navigate multiple rules for how different levels of government interact. By ensuring a consistent relationship between states and the federal government, a lot of complexity can be avoided, which makes governing easier, but also improves legibility.

State Representation

The US senate used to be indirectly elected - senators were appointed by state legislatures. The House of Representatives has always been directly elected, giving people a vote on someone to represent them at the national level, but the senators were there to represent the states. This made the two bodies very different - the decisions people make when electing their state legislature are more localised than those made when electing federal representatives. This meant that the state’s appointees would have different goals and considerations, making the senate an important balance against the power of the federal legislators.

This was changed in 1913 with the 17th amendment to the constitution, making senators directly elected. Whilst some could see this as a victory for democracy, it makes the house of representatives and the senate very similar. Federal concerns can now sway the electorate in both chambers of the legislature, reducing the importance of more local issues in the federal government.

It is understandable that a group of politicians appointing their own representative might make people uncomfortable, however the system pre-1913 allowed for senators to act in the best interest of their states without necessarily succumbing to the winds of populism. The divisive national issues of the day could be debated in the House of Representatives without consuming all deliberations, allowing other necessary governing to be done. Something like this sounds desirable, but raises the question of how to go about generating such a body of people that have national influence, but that can be elected based on local concerns and interests. Avoiding the elections of these people from becoming just another chance to focus myopically on the national wedge issues is difficult once it becomes known that they might wield power at a national level.

One alternative to having their elections be one step removed from the populace, as with the US system pre-1913, would be to have this national power be a secondary role that is eclipsed by the importance of their state role. Whilst no guarantee, this would make it far more likely that people would be concerned with state issues over national issues when voting. State Governors are a possibility here - it is a position that is fundamentally focused around the state, and it is sufficiently important that it is unlikely to be overshadowed by national issues.

In the past, this would not have been a possibility, as each state Governor would have needed to spend the vast majority of their time in their state, making national issues a distraction, and precluding the possibility of spending significant time in the national capital. With the advent of telephones and the internet however, there is no need for them to be physically present. If necessary, they could send delegates to the capital to research and negotiate on their behalf, but the final decision in any vote could still rest with them. As long as state Governors were directly elected, this “Council of Governors” would then be a directly elected body, reducing concerns about lack of democracy.

Summary

Federalism seems like a promising route towards improving the standard of democracy around the world. For any country considering becoming a federation, it will be desirable for them to benefit from all of the positives of federalism whilst avoiding the pitfalls that have caused problems elsewhere. To make good democratic governance as easy and likely as possible, the following points summarise the recommendations from the sections above:

• Composition - encourage states to split large conurbations from rural areas to improve the state government's ability to effectively govern.

• Relative size - limit state sizes so that the most populous state can be no larger than 8 times the population of the least populous state.

• Absolute size - avoid states having populations outside of the range from 200,000 to 25.6 million.

• Adjustment - have a constitutional or federal mechanism for adjusting the borders of states when they reach these limits (that empowers the states to offer their own solutions, rather than providing the federal government with undue power over them).

• Subdivisions - avoid top-level exceptions - if smaller autonomous regions are beneficial, states can always devolve power further.

• Representation - give elected state officials a forum at the federal level so that local concerns can be addressed without being overshadowed by national politics (obviously, this is in addition to national representatives, not instead of them).

Finding the best way to govern a country is an ongoing struggle throughout the world.  The introduction of the concept of legibility suggested that federations might be a good middle ground providing both legibility and democracy for the electorate.  Widening the scope beyond this, there are many other advantages of federations over unitary states.

Antifragility

In Nassim Taleb’s book “Antifragile”, he repeatedly praises federal countries especially Switzerland for their antifragility.  This is an even stronger concept than mere robustness - federal systems with semi-autonomous states not only withstand uncertainty and disruption, but can actually benefit from it.  A federal system allows different policies, systems and approaches to be tried out.  If a system is poor, the state implementing it will perform poorly, but it should not have too much of a wider impact on the country as a whole.  The state can then revert to a previous system or adopt a more successful one tried by a different state.  It is through this natural experimentation and repeated divergence and reconvergence of policy that obstacles can be overcome, and large improvements can be made.

In extremis, the federal government can provide assistance to get the state back on its feet.  In the event that an adopted policy risks causing catastrophe, this fallback should avoid any truly egregious humanitarian cost, but again the catastrophe should be fairly localised to the relevant state, allowing other states to learn from the experience without going through it themselves.  Ultimately, if a system is an improvement, other states are likely to gradually adopt it, but allowing states to do this gradually rather than enforcing it through a centralised unitary system of government allows any kinks to be ironed out and any unforeseen consequences to be explored, without people feeling like they’re being experimented upon by the government.

Freedom

In some circumstances you might expect certain laws to diverge and stay that way - certain communities may like to do things differently, and if that attracts more like-minded people, you can end up with a stable set of laws for one state that are quite different to another.  This variation between states, combined with free movement between the states means that people can vote with their feet as well as their ballot, providing another form of feedback as to which laws are beneficial, as well as giving people greater freedom than the single set of rules handed down by a unitary government.  This goes some way towards the “Archipelago” idea of Scott Alexander (Archive).

The ideal situation from the perspective of freedom, is of appropriate governance at the appropriate level - pushing down power and responsibility to the lowest level of government that can effectively wield it.  This reduces the power of higher levels of government to what is necessary to keep the lower levels functioning well, and is antithetical to the functioning of a highly centralised government.  Of course, smaller units may lack necessary expertise, so things shouldn’t be pushed down to a level that is too low to be effective.

A good example of the idea of “appropriate governance at the appropriate level” is zoning laws - the US often sets restrictions on what kind of buildings can be built at a very local level, resulting in small municipalities lacking the expertise in urban planning to set sensible regulations.  This leads to rules that may seem simple to the regulators, but that result in highly inefficient city layouts requiring everyone to have a car just to go to the shops.  In contrast, zoning in Japan is done at a national level, which allows them to leverage the experience and expertise of specialists to create slightly more complex but flexible rules.  This is not to say that this in particular should be done at a national level - it could be done at a state level if the size of the state were sufficient to enable it to maintain this expertise, but it is a good example of something that the US may have delegated too far.

Political Incubation

In a large country, it can be difficult for anyone to rise to prominence - with no pre-existing smaller structures to gain traction with, prominence and recognition is very much based on either luck (“going viral”) or money (to pay for adverts and exposure).  Whilst this is very much a reality for artists and performers, it is also often the case for politicians, who naturally operate in a divisive and polarised “winner takes all” environment.  A performer may find a sustainable niche with a small number of avid fans, but the spectre of unelectability dooms any politician that cannot break into national prominence.  Too much luck or wealth based success winnows the pool of eligible candidates prematurely, resulting in less skilled and effective politicians, and less choice for the electorate.

On the flip side, rising to prominence in a smaller state is easier - statewide advertising is cheaper than countrywide advertising, and it is only necessary to be electable locally to be able to survive.  Doing a good job locally will allow a politician to generate a positive reputation and wider appeal, rather than relying on a lucky break.  One could argue that a country’s legislature is often made up of local representatives, however these positions necessarily take the politicians away from their local area, and require them to wrangle with national issues that are often divorced from their constituents’ everyday lives.  Few people in the UK can reliably remember who their MP is, so it does little for their prominence.  State governorship however is something that affects people on a day to day basis more than the concerns of the federal government, so a governor or mayor will be more relevant and recognisable to their constituents.  This kind of role also provides politicians with executive political experience at lower stakes than the national stage, giving a wider field of experienced candidates for people to pick from when it comes to national elections.

Proximity to Capital

Politicians usually need to be physically present in the Capital.  If this is too distant from their constituents, it becomes more difficult to spend time with the people they are supposed to represent, so they can become out of touch.  Once they are spending the majority of their time far away in the Capital, it is very easy for them to lose focus on the issues that are important to their constituents, and possibly to even fall into groupthink with the other politicians.  This can lead to areas being underrepresented or neglected, and to undue attention and funding being given to the areas that politicians do frequent, namely the Capital and its surroundings.

Alternatively, if they spend too long away from the Capital, ensuring they have a strong link to their constituents, they will not be “in the room” for important decisions and will therefore not be able to represent them as effectively.  This can again lead to underrepresentation of areas, and a sense that the government is actively ignoring the needs of certain groups.

Easy access to the Capital for the general public is also beneficial to the democratic process.  This can take many forms, but at the very least close proximity is helpful for protesting against or demonstrating for particular policies.  The further away the seat of power is from people, the less they will be able to be physically present, and therefore the less empowered they will be.

Many of these issues have historical parallels, even right back to the Roman Empire. Slightly different problems to those of a modern democracy, but the principles are remarkably similar.  The difficulties of governing a large area from Rome was a factor in several civil wars, and was what drove Diocletian to split the empire into four, with a tetrarch governing each area from their capitals of Milan, Trier, Sirmium and Nicomedia.  

Once Constatine reconsolidated the empire and moved the capital to Constantinople (modern day Istanbul), the east of the empire was able to be stabilised.  This allowed it to persist for another millennium as what we now call the Byzantine empire, but the empire quickly lost control of the western provinces which were too far from the seat of power to maintain effective control over.

With a federal system, although there is still a national capital, there is so much that is devolved to the states that there is a local power centre within each state that allows people easier engagement with the democratic process.  This means that although Washington D.C. receives many complaints in the US, there is much less concern about the government being “Washington-centric” than there are concerns about the UK government being “London-centric”.

Economic Stability

We can extend this proximity argument to economic concerns as well as democratic ones.  In the UK, London receives more funding and more attention than most other areas, and it is hard to argue that this is not at least in part because the politicians are physically there, witnessing issues firsthand.  Other areas of the UK that are comparatively neglected are simply not seen by enough of the politicians for their problems to be taken seriously.

As well as leading to public dissatisfaction and rhetoric about out-of-touch “metropolitan elites”, this unbalanced attention and funding actually exacerbates the problem more.  The Capital will grow and prosper, while other areas decline, giving more people and businesses a reason to leave the declining regions and move to the Capital.  This vicious circle then seems to justify the unbalanced attention - most economic growth will stem from the Capital, so the Capital is seen as “a much better investment” by the government.

Within a federal country, state governments are necessarily spread throughout the country.  This both incentivises the state governments to resolve issues within their state, and provides local employment.  The presence of government functions in a region guarantees a base level of economically active people in that area that other companies and people can rely on.  This reduces the likelihood of an economic downturn spiralling into a mass exodus from a particular region, by providing acyclical employment.

Another economic effect that federal systems introduce is the ability of states to negotiate with the central government to get further civil service jobs or federal level agencies based within their borders.  This can be seen as a negative, often called “horse trading” and “pork barrel spending”, but it encourages critical functions to be spread out, both making them more robust, and ensuring that economic windfalls are not concentrated solely in the Capital region.

The US does this a significant amount, for example NASA has the following sites across the US:  

To its credit, the UK has spread some of its government employment around (the DVLA in Swansea, HMRC in Cumbernauld, etc.), but it is much more able to change this on a whim.  Without a political entity able to argue against a removal of jobs from a region by the central government, this employment is less geographically reliable, and could easily be uprooted by successive governments.

Conflict Resolution

We can see from recent conflicts that attempted to “export” democracy, that states that have had democracy imposed on them in a top-down fashion can be very unstable.  Aside from the inevitable instability induced by this imposition, there is a tendency for such top-down imposition to be done without reference to the existing local systems already in place.  By bypassing existing local systems and structures, whether they are clans with elders or congregations with religious leaders, the local institutions have not bought into the project and may work to undermine it.  These local systems have been around for much longer and have greater loyalty and legitimacy than the newly imposed democracy, so people are unlikely to suddenly feel a connection to the elected central government.  An example of a nascent democracy that is currently in between the “democracy for elders” stage and full democracy is the breakaway region of Somaliland.

Although it is not the only way to end up with a democracy, many stable democratic regimes have started with local institutions. Even where these local institutions are not democratic themselves, their leaders are likely to try to engage with each other on an equal footing, to avoid subservience.  This can lead to the creation of larger institutions that are fundamentally democratic in character (even if it is only the local leaders that get a say).  Eventually, if the democratic nature of these larger institutions is observable, it could lead to movements to democratise the local institutions themselves.  Whilst not necessarily always strictly “federal”, this concept of bottom-up progress towards democracy seems to be possible with much less intervention (and given the examples of Somaliland and Rojava perhaps sometimes with no intervention at all).

In a nascent democracy, the ability of states to govern independently from the national government also reduces the risk of a government trying to subjugate minorities.  After decades of oppression, the Kurdish minority in Iraq have achieved a degree of autonomy through the federalisation of Iraq that was written into their constitution in 2005.  The political autonomy that federalism provides, with some control over their own budgets and rules, ensures that the central government will find it much harder to oppress this minority in future.

In a similar way, the collapse of Yugoslavia demonstrates a failure mode of federalism.  Whilst “balkanisation” is often seen as something to be avoided due to the continued violence in the region after the collapse, the ethno-religious conflicts that it exposed were present in Yugoslavia long before its fragmentation.  This fragmentation can actually be viewed in a positive light - the direct result of a heavy-handed national government trying to limit the independence of its federal subjects.  In this scenario, if a federation must fail, the two most likely outcomes are that the federal government succeeds in centralising authority, or that the individual states secede to become independent countries.  Had Yugoslavia been a centralised state already, any fragmentation would not have had such natural fault lines, and the states would not have had existing governments, making fragmentation much less likely.  In this scenario, the lack of fragmentation simply allows the central government to continue to oppress minorities - it may be less visible, because it would be a “domestic issue” rather than a war between countries, but it is likely to have a far worse humanitarian cost.

With the modern status of “nation states” being the default unit that individuals, organisations and countries interact with, it is very easy to either ignore or underplay conflict that is internal to a country.  When South Sudan seceded from Sudan, it suddenly became apparent how much poorer and more deprived this region was, when this had previously been obscured by aggregated national statistics.  Federalism formalises a structure that reduces the ability of a central government to run roughshod over the rights of some of its citizens, or to simply neglect them, reducing the risk of “Tyranny of the Majority”.

Alternatives

Countries do not have to be either federal or highly centralised - there are a couple of other systems of government that can be considered.  These are confederation and devolution, and it would not be a complete discussion of the benefits of federalism without considering them as well.

Firstly, a confederation is a weaker political union than a federation that explicitly allows secession.  This is good for countries organically coming together to form alliances (eg. the European Union), but it is unlikely to be politically viable for a country itself, as this would facilitate the country potentially losing territory without the need for a complete collapse of the central government.  Governments can of course at any point decide to cede territory, but as with the Scottish independence referendum, this is an active decision on behalf of the central government.  In a confederation, there is legal provision for a state to unilaterally secede, which has the potential to be far more disruptive.

Although there are some countries that refer to themselves as confederations, there are no real confederations currently, with the exception of the EU and possibly Rojava.  Looking at the range of countries that have been confederations at one point or another, it seems more of a transitory status of a group of countries either joining together or splitting apart.  All confederations have historically eventually ended up either forming federations (eg. Switzerland and Argentina) or splitting into separate countries (eg. the United Arab Republic and the Greater Republic of Central America.

Secondly, devolution is a way for a central government to gain some of the benefits of federalism, by giving certain powers to sub-national administrative divisions.  In many ways devolution can serve the same purposes as a federation - if the appropriate governance is devolved, this can be virtually indistinguishable from a federal state for the citizens.

The top level government however always retains the power to legally overrule the devolved governments, and change the devolved powers unilaterally.  This makes the system less robust, being more prone to failure if the central government is compromised.  Structural change can be made more rapidly when a devolved country is not federalised, which might sound positive, but is actually another source of risk.  The central government can enforce adoption of certain policies by all provinces, reducing the “different systems, different approaches” antifragile benefit.  Rapid systemic changes are always dangerous, and although a federation might take more time to implement a beneficial change, their ability to avoid large changes that turn out to be mistakes is a key feature of the system.

Over the short term, if a state is currently highly devolved, it can be reasonably compared to a federal one, but this status can change at any time at the whim of the central government.  With a federal state, the federal nature is very difficult to change, so more likely to endure through the tenure of a federal government that is keen to centralise.

Common Factors

Some of the benefits of federalism listed above centre around different cultures having autonomy to set some of their own rules, avoiding a “one size fits all” approach.  Others are fundamentally related to the fact that regardless of the size of the country, states can be an “appropriate” size.  Large enough to support a functioning government, but small enough for people to feel like their voice matters.  Large enough to have clout with the federal government, but small enough to be allowed to experiment - not “too big to fail”.

These factors suggest that there might be an optimal configuration for any particular country, or at the very least a range of directions in which the configuration can be improved.  Federalism on its own might not be enough to deliver all of these potential advantages - there might be a particular size of state, or method of administration that makes these advantages more likely to materialise.  It is these considerations that I intend to delve into in the next post.

Legibility in the context I am using it here refers fundamentally to the understandability of a system.

It might seem obvious that more understandability is better, but understandability also implies simplicity, and simplicity is not necessarily always good.  For example, with governmental policy, as addressed in James C. Scott’s book “Seeing Like a State” (archive), a drive for legibility can result in adverse situations such as city planners neglecting important complexities that are necessary for a healthy society, or agricultural reforms that promote monocultures and deplete the soil.  This idea of legibility can be applied more widely, to cover any kind of system, process or theory - there is a balance between a theory being legible enough that it can be understood, and being nuanced enough that it gets the correct answers.

Another useful concept to throw into the mix is Philip E. Tetlock’s classification of “Hedgehogs” and “Foxes” (archive).  Foxes are defined as people that have many competing ideas, theories and heuristics which they use to navigate the world and make predictions, while Hedgehogs are defined as people with one big idea or theory, which they try to apply to everything.  In Tetlock’s work, he finds that Foxes are usually much better at forecasting, tending to make predictions that are more accurate, and being less overconfident in their conclusions.  Hedgehogs, on the other hand are found to have extreme overconfidence in their particular theory, despite their predictions often failing to materialise.  I intend to be less critical of Hedgehogs however, as I think their approach, whilst not immediately the best approach for forecasting the future, does have its uses.

Combining these two concepts, it is probably not too much of a stretch to describe Hedgehogs as seeking legibility, and Foxes as being comfortable with illegibility.  As a Fox, if you have many theories, how do you know which one to apply?  Even if your heuristics work very well to predict the world, it is difficult to explain them to someone else, therefore illegible.  On the flip side, as a Hedgehog, you can explain your thinking very easily, making it legible - you apply your theory, and it generates a prediction. Your ability to predict things however, is entirely dependent on the strength of your theory, which may not have enough depth to fully capture all of the nuances of reality.

In some ways, the collection of heuristics that Foxes use is analogous to culture and tradition referred to by Joseph Henrich in “The Secret of Our Success” (archive). The heuristics promoted by a culture can be very powerful, but without them being legible, they are hard to justify to outsiders.  Asking ordinary people in a tropical country "What is the point in ritually washing this vegetable before cooking with it?" is unlikely to get you an answer like this. This can also be seen as a justification for the precautionary principle of Chesterton’s Fence - just because a heuristic, process or structure is not legible doesn’t make it useless.

In a world of only extreme Foxes, we would be able to make reasonable predictions about things, but explaining why we think what we think would be difficult, in much the same way that explaining why exactly the weights on the nodes of a neural net allow it to recognise text correctly is a virtually impossible task.  A world of only extreme Hedgehogs on the other hand, would have a selection of understandable theories and methodologies for approaching the world, which would likely be applied with confidence, followed by catastrophe as reality collided with the overly simplistic approach, just like High Modernism.

I think it is fair to say that both science and society work best somewhere in the middle, with a mixture of both approaches.  A less extreme Fox might be happy using different maps for different purposes, but be slowly trying to iron out areas where they contradict, just as a less extreme Hedgehog might prefer to use one map for all purposes, but be slowly trying to incorporate other details into this map that are missing but useful.  Fox thinking may be much better for predictive purposes, but Hedgehog thinking is clearly more focused on trying to combine theories into a cohesive whole, which is a valuable project for increasing legibility. As you may be able to tell from the multitude of links to Scott Alexander's blog above, this is a theme that he has written extensively about (archive).

II. Finding a Balance

When trying to systematise the world, it is to be expected that any theory will get worse before it gets better.  First we have a set of illegible heuristics that work quite well, then we try to come up with a theory that is legible instead.  This legible theory does a worse job of modelling the world than the heuristics did, but some Hedgehogs use the theory anyway.  These people inevitably fail, but through their failures demonstrate where the theory needs improvement, adding complexity to the theory, but resulting in slow incremental gains to the accuracy of the system.

Eventually, we might end up with a theory that works as well as (or even possibly better than) the heuristics we started with, but this takes a lot of time, and a lot of heroic failure on behalf of Hedgehogs.  A theory develops over time until it incorporates enough complexity to be acceptably accurate, but it is no good noting that a theory does an inadequate job, and condemning the idea of seeking theories entirely.  While a failure mode of Hedgehogs is being overconfident in an insufficiently comprehensive theory, or refusing to update a theory that has proved inadequate, a failure mode of Foxes is not even trying to find a model for something, or not caring about an obvious contradiction between different heuristics.

This suggests finding a balance between legibility on one side, and accuracy and effectiveness on the other - a sweet-spot where people can understand what is going on well enough to do what they need to, but also be sufficiently accurate.  As theories and systems become more complicated, they risk slipping back into illegibility once more, at least for non-specialists.  Most people could get to grips with Newtonian Mechanics, but very few can become fully comfortable with General Relativity.  In this sense, although General Relativity has made black holes and curved spacetime legible to some physicists, it is effectively an illegible heuristic to most people.  Newtonian Mechanics is more legible, and is acceptably accurate for most scenarios, even though in theory General Relativity is a better model.

The same concept applies to systems such as a legal code - laws are usually legible to lawyers, but are sufficiently complex that ordinary people view the legal system as a black box handing out judgements.  A legal system that is too simple would not work for anyone, as there are too many edge cases that must be considered.  The tendency of laws to be written in “legalese”, renders them effectively in a different language, despite the fact that this makes them much more robust.

Just as someone using Newtonian Mechanics could hire a physicist when they get too near a black hole, if there were a more universally legible version of a legal code, this would better enable people to interact with the law, whilst still allowing them to hire a lawyer if they got too near an edge case, providing a sweet-spot of both legibility and effectiveness. In fact, having a parallel document to the law itself, consisting of non-legalese, straightforward descriptions of the laws listed, would make for an excellent addition to the current legal system in many countries.  This could be entirely subordinate to the law as written in legalese, so there would be no ambiguity if it was unclear, but it would simply give ordinary people the ability to understand in broad strokes the laws which apply to them.

Of course, in the UK, the law is already unusually illegible anyway - a combination of statute law, common law and case law, some of which is not even publicly accessible.  Add to this multiple layers of amendments of the form “replace paragraph 2 subsection 3 with the following text…”, which are often not actually incorporated into the main document (this would require a separate act of parliament).  Clearly UK law is in dire need of being made more legible to lawyers themselves, before mere mortals stand a chance at getting a non-legalese version.

III. Legibility in a Democracy

If we apply this principle to democracy, we can get some interesting insight.  A highly centralised democracy is very legible - people vote for the leader, who appoints whatever officials they require.  Very simple and understandable.  Firstly however, this centralisation brings with it the downside of inflexibility - if different areas need different treatment, the leader needs to fully understand all the issues to be able to treat them correctly.  Without this understanding, they may attempt a “one size fits all” approach which causes unnecessary inefficiency and strife.  Even aside from the downside of inflexibility that centralisation brings, this simplicity makes it fundamentally not very democratic - you are effectively periodically electing a dictator, and with so much concentrated power, it is quite possible that one of these temporary dictators finds a way to make it more permanent.

Another very legible democracy is one where every decision and law is put to a plebiscite based on a simple majority.  Again, aside from the enormous inefficiency of this system, it is similarly not actually very democratic - without any mechanisms for compromise, consensus building or minority protection, this suffers enormously from the problem of tyranny of the majority.  A sufficiently polarised society using this system is easily comparable to one consisting of 51 wolves and 49 deer - a vote on whether or not to eat the deer would be easily passed by a majority.  Without a robust system of checks and balances, this overly simplistic system can easily turn into a tool of oppression.

Looking at the other end of the spectrum, the UK is a good example of a really quite illegible democracy.  Firstly, the executive government is not directly elected, but formed out of a group of local legislative representatives, in an opaque process behind closed doors.  This blurs the lines between setting the laws and running the country, and sometimes makes the decision of who leads the country very unpredictable.

Secondly, local government is dealt with on a hugely inconsistent basis - there are multiple sub-national entities, each with different powers.  Scotland has a parliament with a great degree of autonomy, but is still governed in part by the parliament of the UK.  Northern Ireland, Wales and London have assemblies with some devolved powers, and some other large cities have directly elected mayors.  Powers are split between these entities of varying seniority, and local councils, some of which are the smallest unit of government (Unitary Authorities), and others are split into two levels (County Councils and District Councils) with different responsibilities.

This means that if you live in Kirkcaldy, government functions may be performed by the unitary Fife Council, the Scottish Parliament or the UK Parliament, whereas if you live in Skipton, they may be performed by Craven District Council, North Yorkshire County Council or the UK Parliament.  There is no level at which these powers are consistent - even at the very top, there are powers the UK Parliament hands to the Scottish Parliament, but which it keeps for all other areas.  To add insult to injury, this is still not the end of it - Post Codes are used for a wide range of purposes, many unrelated to the postal system, but are far from coterminous with county or district boundaries, and counties are grouped together inconsistently for a wide range of administrative purposes, as per this magnificent monstrosity from artist/cartographer Alasdair Gunn:

For anyone to successfully interact with this system, they need specific knowledge of the local structure, which is not necessarily transferable to another jurisdiction.

IV. Federations as a Middle Ground

If we try to find the sweet-spot in the middle, we can consider some other countries - France’s democracy is very centralised, and therefore very legible, but not quite so simplistic as the first example above.  There are local representatives as well as an elected president, but unfortunately this still requires the heavy machinery of the central government to get bogged down in the minutiae of far flung and unique environments such as Corsica, Mayotte and Guiana.  The effort needed to administer such places is disproportionate to their population, causing inefficiencies, but not administering them would be neglectful, leading to its own problems.

Alternatively, we can look at the US - a federation.  Here, we have aspects of illegibility - each state has its own laws, which may differ from its neighbours, but at the same time, each state is treated consistently by the federal government.  This means that although people moving between jurisdictions may need to learn multiple sets of rules, there are constants - they are always interacting with the federal government in the same way.  It is an ongoing source of disagreement in the US, exactly how much is centrally controlled vs. how much is state controlled, which is often portrayed as a disagreement about the “strength” or “size” of the federal government, but this could easily be portrayed as a disagreement about the overall legibility vs. flexibility of the system.

Zooming in even further, we see even smaller structures - counties and municipalities, which administer certain devolved decisions and services themselves.  Again it is a decision to be made how much is devolved, and how consistently.  The benefits of flexibility are great, so I am personally inclined to see things devolved as far as is practical, with no government function being performed at a higher level than is necessary to facilitate sufficient coordination, however this must be balanced against the need for a certain bare minimum level of legibility at each level of government.

Even if at each level of government, the level below is able to have variable rules and approaches, the relationship between the units and subunits of government should be kept as consistent as possible, to leave the structure of government legible.  One US state may be split into “counties”, to which certain powers are devolved, and another into “townships”, to which different powers are devolved, but each state has the same powers devolved to it by the federal government, and each subunit has the same powers devolved to it by the state.  Having both “counties” and “townships” as first-level subunits of the same state would be a recipe for confusion, as it is with Unitary Authorities, Counties and Combined Authorities in the UK.

To have a populace that is democratically engaged, a certain amount of legibility is critical.  Politicians should make it easy for people to interact with their government, which means giving them minimal sets of rules to learn, and making it easily understandable which level of government they need to interact with for different purposes.  If people live in one area and work in another, they may cross a state or county line, therefore having to interact with two separate jurisdictions with different rules, but if the structure of government is consistent, they can at the very least know what they do not know.

Clearly, if states are too small, people may need to interact with more than two different states, which again becomes unwieldy (for example, 7 Swiss cantons have both a population less than 100,000 and an area less than 1000 square kilometers).  Unlike smaller units such as counties, which tend to have mostly administrative powers, states can have a huge amount devolved to them including taxation and writing laws, allowing for significant differences which must be learned.  In a federal system therefore, finding both the right sizes for states, and the right powers to devolve to them is very important to ensure that the populace has the right balance of flexibility and legibility to remain democratically engaged.

V. Legible for Whom?

Another attempt at balancing the need for legibility with the need for effectiveness is technocracy.  This approach has highly specialised people, to whom more complex systems are able to be legible, with the hope that they can come up with “the best solution”.  This becomes difficult for the public to understand however, which then conflicts with the ideals of democracy.  Singapore’s approach here was to take unpopular but necessary actions that were so successful that people were won around to them before they turned against the government.

This has worked for Singapore, but is not necessarily a guaranteed approach for several reasons.  Firstly, even if a country is careful not to predominantly recruit technocrats from more economically advantaged groups in society, they are still likely to diverge culturally from the rest of the populace over time, becoming out of touch, less representative, and optimising for the wrong things.  Secondly, it is possible for technocrats to become overconfident in their theories and abilities, due to “echo chamber” like effects, allowing for mistakes similar to High Modernism.  Finally, the greater the impact of a policy and the more uncertainty there is around which approach is best, the more it is worth testing before full country-wide implementation - this would slow the process down, giving more time for opposition to form, which either results in beneficial policies never being implemented, or in the government implementing things without testing with negative consequences.  E. Glen Weyl writes further on the problems with technocracy, but needless to say, for all the potential benefits of a technocracy, if people don’t understand what is going on, it cannot be very democratic.

Whilst legibility supports public engagement, too much legibility allows demagogues to offer easy solutions.  Simplifying things to cater to the lowest common denominator (a busy person with no time to spend understanding the nuances of policy) doesn’t allow for informed debate either.  It is desirable to strike a balance between legibility and effectiveness. For this, you need people with enough time to invest in understanding the issues, whilst still being representative of the populace as a whole - not a political class (susceptible to populism, looking for easy answers), or a technocratic class (susceptible to overconfidence, lacking the insight from ordinary people).

VI. Sortition as a Solution

One potential solution to this balance is sortition - the way representatives used to be selected in ancient Athens.  This is a process similar to that used for jury duty, in which a number of members of the public who are citizens in good standing are selected at random to perform their civic duty.  Using sortition to select democratic representatives avoids the rat-race of election or re-election, reducing the pressure to pander to populism.  Its advantages are not simply limited to this however - the representatives being randomly selected from the population all but ensures that the majority of representatives are ordinary people, very much in touch with the wants and needs of the average citizen, rather than out of touch career politicians or technocrats.  Furthermore, given a large enough random selection, it can be made highly statistically likely that the selected people are a good representation of the population at large, which makes it likely that all interest groups are being represented.

It could be argued that since ordinary people do not tend to take the time to understand the nuances of policy normally, this would be a disaster.  However in the case of jury duty it is usual for people to take this civic duty very seriously, and when given leave from their job to perform this function, they have the time to look into any nuances in order to better understand them and make informed decisions.  In fact, there are studies suggesting that politicians that are more open minded and receptive to new perspectives may be less successful at being elected, which may mean that the amount of nuance that politicians are likely to be able to understand is less than that of the average person.

When preparing for the Marriage Equality referendum in the Republic of Ireland, the government made heavy use of focus groups that were representative of the population at large. This was in order to ensure that they understood the concerns of every different demographic, to allow them to put across the proposed constitutional amendment in a way that wouldn't alienate large groups of people. In comparison to a previous referendum that failed, this article states:

The main thing that emerged... was that voters had a range of fears that they never got a chance to articulate.

By ensuring that ordinary people from all walks of life are included in the process of governing and lawmaking, sortition could dramatically reduce both the issue and the perception of politicians being out of touch.

In short, legibility is a desirable quality for any democracy, because for the public to be able to decide how they should be governed, they must first understand how they are governed.  Seemingly in opposition to this however, are demands for effectiveness and resistance to exploitation, which are also fundamentally necessary for any stable democratic system of governance.  Federalism and sortition seem to be very promising candidates for mechanisms that (if implemented in the right ways) could satisfy both sides of this trade-off, allowing for a large amount of legibility whilst still being flexible, efficient and difficult to exploit.

Utilitarianism - A Brief Background

My aim here is not to provide yet another response to all of the common challenges to Utilitarianism.  A fairly good background of the challenges Utilitarianism has been faced with over the years can be found by reading through its Wikipedia article.  Alternatively for an even deeper dive, this article gives a very thorough summary of such things.  The issue is, that having fended off these initial criticisms, the philosophy of Utilitarianism has encountered a few problems which are not so easily dispatched.  Of the different types of Utilitarianism, some resolve certain problems, and others resolve other problems, but all reveal their own cracks in turn. It is on these deeper issues that I intend to focus.

That being said, I will at least spend a couple of paragraphs on the more straight-forward criticisms, so that it doesn't seem like I am brushing them under the rug. As such, feel free to skip to the next section if that doesn't hold any interest for you.

Utilitarianism is a very compelling system of ethics, both for its seeming simplicity, and for the fact that most of its proponents have been demonstrably far ahead of their time regarding many moral questions (e.g. Jeremy Bentham’s views on animal rights, and John Stuart Mill’s views on gay rights).  It is also much more resilient to challenges than many people initially expect. Upon first hearing about Utilitarianism, people often raise objections to it on relatively simplistic grounds, perhaps not realising that as a philosophy it has been around since at least the 1780s. Through over 200 years of careful deliberation, it has evolved into a cluster of philosophies that have developed a significant following in various different communities.

Many challenges take the form “what if situation X occurred - Utilitarianism would tell you to do Y, but this has bad consequences.”  As a form of consequentialism, the answer to this is very simple - why does the presence of this bad consequence not have a coefficient in your utility function?  Once this is included, Utilitarianism no longer suggests taking action Y, as its consequences are bad. Even the question “what if taking the time to consider the utilities of different actions causes negative consequences?” can be answered by simple pragmatism.  Of course you can’t do a full utilitarian calculation around every action you ever take. Ethical rules are very useful, and we can use Utilitarianism to work out which rule sets result in the best society. There may be occasional grey areas where the rules don’t give clear answers, at which point it becomes far more reasonable to fall back to the calculation. This is a perfect example of the Law-Morality-Axiology hierarchy in action (archive). In fact, this is referred to as Two-level Utilitarianism, a synthesis of two earlier viewpoints - Act Utilitarianism and Rule Utilitarianism.

Addressing More Stubborn Issues

Whether you subscribe to Hedonic Utilitarianism or Preference Utilitarianism (or indeed, the somewhat more fuzzily defined Ideal Utilitarianism), there is still the question of whether you are interested in maximising the average utility, maximising the total utility or minimising negative utility.  You can construct a thought experiment in which Total Utilitarianism would be happy to fill the universe with clones or utility-bots, or even just with people that were only-just-happy, in a kind of Malthusian race to the bottom. Equally, with Average Utilitarianism, under some conditions painlessly killing people (even ones with positive utility) might be justified, if it improves the average level of utility. Both of these scenarios are commonly referred to as the "Repugnant Conclusion".  Negative Utilitarianism gives rise to thought experiments in which it is desirable for humanity or even all life to die out, if certain amounts of suffering are unavoidable (though there are some fairly sensible attempts to avoid this conundrum).

Therefore, my objective is to resolve some conflicts between Negative Utilitarianism, Average Utilitarianism and Total Utilitarianism, whilst attempting to synthesise Preference Utilitarianism and Ideal Utilitarianism by explaining why people might sacrifice themselves to protect monuments or knowledge from destruction (e.g. Library of Alexandria, Sack of Rome, Palmyra), and why people value "being remembered" and their legacy/long term impact on society.

So here goes:

• People are defined by their minds and their bodies.

• People's bodies are described by their DNA.

• People's minds are neural nets, which are described by the matrix of values at each of their nodes.

• From someone's DNA and neural net matrix, it should (at least hypothetically) be possible to recreate them.

• Therefore people are data.

• If people are data, people dying is data loss.

• Further to this, people produce additional data over the course of their lives.

• Works of art can be described by data.

• Scientific progress is the steady accumulation of data.

• Importantly, suffering is still a key element of the utilitarian calculus - suffering is bad.

This gives us a useful starting point - as well as caring about happiness or the removal of suffering, it seems that in an abstract sense we already naturally care about data.  Based on this train of thought, data loss is bad and should be avoided.

Replacing Subjective Value Judgements with Data

Looking at Ideal Utilitarianism, the view is that some things have greater worth than simple hedonistic “lower pleasures”.  A lifetime spent in ecstasy is judged as in some way inferior to a life of discovery, or a life creating beautiful art. In this sense, data becomes a more rigorous objective than the concept of “intrinsic good” - it separates the pleasure of creation or of making a discovery from the “worthiness” of the creation or discovery, as well as giving us a metric which might allow us to assess some aspect of worthiness. We then need to determine some sort of conversion rate between pleasure and data.

Once separated from the “worthiness” judgement, I personally find that the concepts of pleasure and intrinsic good (with worthiness factored out) map fairly well onto Herzberg’s Hygiene and Motivational Factors model. You can only become so happy by satisfying the hygiene factors (lower pleasures), and beyond that point you are wasting effort and resources. Motivational factors (higher pleasures/intrinsic good) can only come into play once the hygiene factors are satisfied, enabling one to reach a much higher level of happiness.  This allows for the recognition that a life of discovery can be quite rough, and could be improved by a little hedonism, despite being entirely worthwhile, as well as the recognition that whilst it can be very fun to rediscover something for yourself that has already been established, it is even better to discover something new, creating new data rather than backing up the old.

Valuing data also allows for Preference Utilitarianism - if someone prefers to suffer, in order to generate more data, this can be acceptable.  Hedonic Utilitarianism would try to stop people from suffering, even if they wanted to, denying free choice, but allowing for data to be another component of utility, allows for a balance between data and suffering.  It also resolves the issue around death - whilst we might associate dying with suffering, as soon as we are dead we do not suffer any more. Death may cause suffering to those who care about us, but if the entire planet was incinerated, who would care?  Valuing data itself, and seeking to avoid data loss as another key consideration alongside utility resolves this, viewing any death as negative, as this is the loss of the data that defines that person.

Δεδομένα

What I am considering is therefore a slight adjustment to Utilitarianism, in which as well as maximising utility or minimising suffering, we also aim to maximise data or minimise data loss.  Whilst this does complicate things somewhat (how much data is one utilon worth?), it keeps the fundamentals of the system as simple as possible. This has the potential to give us a more complete framework, of which we could view Preference Utilitarianism and Ideal Utilitarianism as facets.  They are effectively projections of the full system that look similar but disagree in places because the fundamental nature of the system is hidden. Much like seeing the shadow of a cube, and seeing a square one moment, and a hexagon the next.

For want of a better term, I refer to this as Dedomic Utilitarianism, from the greek “δεδομένα” meaning data.  I considered “Data-oriented Utilitarianism” or similar variants, but this makes it sound more like computer science than philosophy.  Dedomic Utilitarianism then stands as an alternative to Hedonic Utilitarianism, accepting a slightly more complicated, but hopefully still a reasonably objective definition of what we consider to be good.

Diversity vs. Redundancy

Every animal, plant, race and culture is able to be defined by some sort of data blueprint, and is demonstrably able to exist in some environment.  The environments in which they succeed and fail, and the advantages they confer under different scenarios make them valuable data to anyone trying to find ways to improve the world.  This sets them apart from random noise, which for these purposes is not data. Diversity is therefore data. Homogeneity and uniformity are redundancy - some redundancy is useful for guarding against data loss, too much redundancy is a waste of resources.

At this point it is worth mentioning entropy - random noise is high entropy and data is low entropy, but homogeneity is also low entropy, so it is not sufficient to simply minimise entropy.  In fact, minimising the increase of entropy is a corollary of Utilitarianism. Entropy always increases, and low entropy is a precious resource that we should spend wisely - if we take actions that give us utility or data but cost a lot of entropy, when there are less expensive ways to generate the utility or data, we could have taken the less expensive actions, and generated more utility or data over the long term.

How Does it Stack Up

Having roughly described the idea behind Dedomic Utilitarianism, it is worth seeing how it stacks up against the issues we raised earlier:

• We observed that Negative Utilitarianism would prefer to destroy the entire universe if it were found to contain too much suffering.  Dedomic Utilitarianism says that this would result in massive data loss, therefore a higher bar of suffering is required to justify such a conclusion.

• Average Utilitarianism would suggest that under some conditions, painlessly killing people might be justified, if it improves the average level of utility.  Dedomic Utilitarianism says that killing people is data loss, so they would have to be suffering significantly to justify this.

• Total Utilitarianism would be happy to fill the universe with super-happy clones/utility-bots.  Dedomic Utilitarianism says that this is redundant - the additional clones/bots do not add anything other than improving resilience against data loss, which has diminishing returns as duplication increases.

Taking a common thought experiment, we can see whether it stacks up against our intuition: if you were cloned in a teleporter malfunction, what would the ethical implications of painlessly terminating one of the two of you be?  Dedomic Utilitarianism gives us the answer that it depends on when the termination happens - if it is immediately after the duplication, it is only a minor concern, as you are identical, so no data is being lost, you are just losing some potential for redundancy.  Later, and your two different minds will have started to diverge due to different experiences - the longer the two of you exist, the more different you will become, and the more data loss will result from one of you being terminated. In the extreme case, this starts to look like having an identical twin.  Identical twins are different people, who share DNA - although the DNA is duplicated and therefore beneficial only through improving redundancy, the mind's configuration is a much larger factor in the quantity of data, and this data is much more likely to be highly different to that of the other twin, making preserving their existence worthwhile.

Further Considerations

So far, I have been rather vague about whether we are trying to maximise utility or minimise suffering, and whether we are trying to maximise data, or minimise data loss.  This is not obvious, but as far as utility goes, people's happiness tends to renormalise, so we are usually left seeking a greater high. Contentedness and lack of suffering seems more tractable and well behaved, so minimising suffering seems the safer option.  As far as data goes, minimising data loss would result in lots of redundancy, whereas maximising data would allow for some redundancy, whilst also seeking progress.

Under Dedomic Utilitarianism, I am therefore inclined to propose that we are trying to minimise the suffering of conscious beings, whilst maximising data.  This approach aligns well with intuitions about people being very unhappy when their legacy is destroyed, the value of stored knowledge and monuments, and our views of the kind of people that would seek to destroy them.

A few further questions to ponder:

• Should we care if people's minds are "put on ice"?  To me this seems preferable to being destroyed through death or data loss.  If you are never booted up again, this is unfortunate, but your data can still be useful for other conscious minds to work out how to be happy and not be unhappy.

• Should we care if data exists but is inaccessible?  If inaccessible means permanently lost, I would view this as data loss, therefore bad.  Something outside the cosmological horizon is permanently lost for all practical purposes given our current understanding of the universe.

• Do we care about data because of its use to conscious minds, or just for itself?  Personally, I think I still care about its use to conscious minds. Perhaps the theory might be purer if this were irrelevant, but I feel like an ethical system in the absence of conscious minds is a little pointless.

How do we value data? The human genome contains around 1.5GB of data.  The human brain contains around 100 billion neurons each of which can have 10,000 connections.  Making a very rough estimate for the amount of data it would take to fully define someone’s brain, let’s take every possible pair of neurons in the cerebellum (roughly half of the total neurons), and assign it a 1 if the neurons are directly connected, and a 0 if not.  The number of pairs of neurons is 50 billion choose 2, which is approximately 10^21, but presuming that of the 10,000 connections they can each have, these tend to be some set of their 1 million closest neighbours, we can get a figure of 50 billion x 1 million which is 5x10^16.  This gives us 50 ExaBytes. Both of these probably have a lot of redundancy however - your genome is more than 99% the same as everyone else on the planet, and it is possible that the data that makes up people’s brains could be compressed significantly too. It becomes further complicated when we consider knowledge - some data is clearly more valuable than other data.  The laws of general relativity may be able to be written very concisely, but if we lost that knowledge and had to re-discover them, that would take a long time and a lot of effort. Perhaps the value of data is given by the entropy increase it would take to re-acquire it.

This question, and the question of how the value of data compares to the value of utility are both difficult, but probably worth investigation.  Despite inevitable uncertainty, I am sure that reasonable upper and lower bounds can be found, that allow for useful discussion and calculation.

I. Normality

The “Normal Distribution” (also called the Gaussian Distribution) is a very useful and well-studied tool for analysing data.  It is however often misapplied, despite the efforts of Benoit Mandelbrot and Nassim Taleb to raise awareness of areas where it might be inappropriate to use.  One reason people may be tempted to overuse it might be its name, which is a little too suggestive of it being some kind of “standard”, so henceforth I will use its alternative name to avoid perpetuating this any more than is inevitable.

The trouble is, that everyone is so familiar with the Gaussian Distribution, that it is very seductive to shoehorn your data into it and try to use the familiar techniques to analyse your data.  When people see a “bell curve”, their first thought is usually “looks like it is Gaussian distributed”, meaning that the data behaves like it has been sampled from the graph below:

There are however many other distributions that are “bell curves”, and therefore look very similar to a Gaussian Distribution.  Some of these behave very differently indeed when compared to the Gaussian Distribution, so it is important not to just default to using the Gaussian Distribution as soon as you see something that looks like a bell curve.  By way of example, below are just two examples of distributions that are bell curves, but have very different behaviours to the Gaussian Distribution (in blue).  The “Cauchy Distribution” is in green, and the “Students’s T Distribution with 2 degrees of freedom” is in red:

There is a fun bit of analysis that the data scientist Ethan Arsht did, comparing different military commanders throughout history to determine some sort of ranking for them, in a similar vein to baseball sabermetrics. To be clear – I like this analysis. It is a pretty neat insight, and took Ethan Arsht a lot of time and effort to put together, so I am not denigrating him or his conclusions in what I am about to say. It is just a perfect example of the kind of thing I am talking about, that lots of people do without really thinking about it (so, if you’re reading this Ethan, I apologise for using you as an example – there were probably lots of other examples I could have used).

In this article, he writes that the different commanders’ scores “largely adhere to a normal distribution”, and that Napoleon’s score is almost 23 standard deviations above the mean. The probability of an event occurring that is at least 22 standard deviations above the mean whilst being Gaussian Distributed is:

This is an incredibly minute number. For perspective

This means that if every single particle in the universe represented a new military commander every single millisecond since the big bang, we would only have seen

military commanders so far, making it close to a 1 in a million chance that we would have encountered a single Napoleon in the entire history of this bizarre hypothetical universe of short-lived commander-particles.

The point of all of this, is that if you get an event that is almost 23 standard deviations above the mean assuming a Gaussian Distribution, then your data is NOT Gaussian Distributed.  Even if you get an event “only” 6 standard deviations above (or below) the mean, this has a probability of around 1 in a billion, so unless you have an enormous amount of data already, it is pretty reasonable to suggest that your data isn’t as well behaved as a Gaussian Distribution would be.  There is a good post on Slatestarcodex (still available in this archive) on conceptualising very small probabilities, which is useful for gaining a bit of intuition on the matter. Effectively, if the data was truly Gaussian Distributed, the outcome above is so vanishingly unlikely that it becomes more likely that you have either made a mistake in the analysis, or are simply hallucinating the whole thing.

II. Portioning

The most important way in which these other distributions differ from the Gaussian Distribution is how “heavy” their “tails” are.  This basically means how quickly or slowly the probability declines as you move out to the far right or left of the distribution, and should be fairly easy to pick out on the graph above.  If a distribution has heavier tails than a Gaussian Distribution, then more extreme events are more likely.  Importantly, this is not the same as variance – a Gaussian Distribution with a high variance might permit a wide range of events with a reasonable probability, but an event that is 6 standard deviations above the mean is still around 1 in a billion.  A heavy tailed distribution could be constructed to have the same variance, but such an event would be significantly more likely – perhaps 1 in 1000.

A useful concept to get across the idea of heavy tails is referred to as “portioning”.  People’s heights can be considered to be roughly Gaussian distributed (we can ignore the fact that sexual dimorphism makes the distribution of heights bimodal, as this doesn’t significantly impact the tails).  If someone selects two people at random from a population, add their heights together, and that sum is all that they tell you, you can make an educated guess about what you expect the individuals’ heights to be.  If the sum is unusually large, say 400cm, you know that 200cm people are quite rare – around 1 in 1000, so picking 2 of them would be 1 in a million.  On the other hand, whilst it could be an average height person at 175cm and an extremely tall person at 225cm, people that tall are more like 1 in 100 million, so given that the sum you were given is 400cm, unlikely though that result was, it is much more likely that the people measured were both very tall, around 200cm each, than it is that they managed to measure one of the vanishingly few people that is around 225cm tall.  This is described as “even portioning”.

Wealth however is distributed according to a heavier tailed distribution – if you did the same thing but with people’s wealth rather than their height, and were given the sum of $1 billion, it would be possible for it to be two people each with wealth around $500 million each, but each of these is 1 in 300,000 making the probability of picking 2 of them 1 in 90 billion.  Picking a person worth around $1 billion would be around 1 in 600,000 making it far more likely that the people were 1 average person and 1 billionaire, given the sum that you were told.  This is described as the “concentrated portioning” – the majority of the sum is concentrated into one of the portions making up the sum.  This concentrated portioning is a feature of heavier tails, and can generate useful intuitions about heavier tailed randomness.  If you add more people/samples to the sum, the portioning may even out, with several samples contributing significantly to the sum – this is referred to as having concentrated short-run portioning but having even long-run portioning.  If the tails are even heavier though, one sample could still dominate, contributing most of the sum’s value, no matter how many samples are summed together – this is referred to as concentrated long-run portioning.

III. Tail Terminology

Along the road to generating a structure from which to better perceive these concepts, there is some existing terminology that needs discussing, if only to immediately ignore it in favour of something better (seriously, feel free to skip to the next section).

Heavy tails technically means any tail that decays more slowly than that of the Exponential Distribution (it is defined in slightly more complicated and rigorous terms involving it’s “moment generating function”

but decaying slower than the Exponential Distribution is basically the end result). The Exponential Distribution is itself slightly heavier tailed than the Gaussian Distribution, but it is still fairly well behaved – it exhibits short-run concentration, but is even in the long-run.

Long tails are defined slightly differently, being distributions that obey the following formula:

This means that if the sample surpasses some high value, the probability approaches 1 that it will surpass any other higher value as the initial high value approaches infinity, or put more simply – “big events are likely to be even bigger”. This results in the vast majority of heavy tailed distributions also being long tailed, but it is technically possible for a distribution to be heavy tailed without being long tailed, if you contrive to make it irregular enough.

Sub-exponential tails are defined differently again, being distributions satisfying the formula:

This actually turns out to be an equivalent statement to having concentrated short-run portioning in the case where N=2 (the shortest possible run). Again, the vast majority of long tailed distributions are also sub-exponential, but it is technically possible to construct a long tailed distribution that is not sub-exponential.

We now have three terms that are almost equivalent to each other, but not quite. This is not useful for generating any kind of helpful structure, and it is not too surprising that heavy tails and long tails are used fairly interchangeably in most contexts. Aside from highly contrived distributions that are constructed solely to prove that the different definitions are not entirely equivalent, all commonly used distributions that are members of one of these sets are members of the other two sets as well. As being heavy tailed is the most inclusive set, I have chosen to use this terminology, but we ideally need something more informative.

One final term that can be used is fat tails. This is sometimes used to mean a tail that decays like (or slower than) a power law, such as a Pareto Distribution. This would make it refer to a significantly heavier tail than many sub-exponential distributions, and could potentially be a useful classification if it could be used unambiguously. Unfortunately, it is also often used synonymously with heavy tails, which removes any useful disambiguation properties it could have had.

IV. Mandelbrot’s Seven States of Randomness

Thankfully Benoit Mandelbrot developed a system of classification for types of randomness that allows us to classify different types of heavy tails much more reliably. It is still not particularly widely known about, but recent efforts by Nassim Taleb have spread the concept slightly beyond the academic community. The main issue with the classification system as a conceptual structure is that it is not particularly easy to visualise, and requires a relatively deep understanding of probability and mathematical terminology to work with. Mandelbrot started with 3 states – Mild, in which short-run portioning was even; Slow, in which short-run portioning was concentrated but long-run portioning became even; and Wild, in which long-run portioning remained concentrated. He then expanded upon this and in his book “Fractals and Scaling in Finance” Chapter E5, section 4.4, Mandelbrot lists “Seven States of Randomness”, which I have paraphrased below:

• Proper Mild Randomness

  • Short-run Portioning is even for N=2

• Borderline Mild Randomness

  • Short-run Portioning is concentrated

  • Long-run Portioning becomes even, for some finite N

  • The n^th root of the n^th moment grows like n

• Delocalised Slow Randomness

  • The n^th root of the n^th moment grows like a power of n

• Localised Slow Randomness

  • The n^th root of the n^th moment grows faster than any power of n

  • All moments still finite

• Pre-wild Randomness

  • Moments grow so fast that some higher moments are infinite

  • The 2^nd moment (variance) is still finite

  • Long-run Portioning still becomes even, for a large enough finite N

• Wild Randomness

  • Even the 2^nd moment is infinite, so the variance is not defined

  • There exists some moment (possibly fractional) μₘ, m>0 that is still finite

  • Long-run Portioning is concentrated for all N

• Extreme Randomness

  • All moments μₘ, m>0 are infinite

The first couple of these make sense, given our understanding of portioning, but then they start being defined in relation to moments, so before moving on, let’s take pause to understand what this is saying (or skip to the next section, if you want to see a more intuitive approach). As a side-note, it is worth mentioning that “Delocalised” and “Localised” also refer to properties of moments of functions in these classes, however it will not be necessary to delve into the reasons behind this terminology, as other ways of defining these categories may be much more straightforward.

Firstly, the area under a distribution's Probability Density Function is always 1 by necessity. The x-axis covers every possible eventuality, therefore the probability of an event occurring that is anywhere on the x-axis is a certainty. This means that for any Probability Density Function f(x), we have the identity

which can be referred to as the 0^th moment.

The mean of a distribution is calculated with the formula

and is known as the first moment, whilst the variance

is the second central moment, closely related to the second moment

More generally the nth moment is defined as

and we can extend the concept to fractional n where this formula is still well defined.

This is the starting point for Mandelbrot’s definition of the later States of Randomness – if we create a new function based on these moments, giving us the x^th root of the x^th moment:

we can investigate how rapidly it grows, and compare it with other well known functions such as xⁿ or eˣ.

The way to reliably compare functions in this way, is to look at their behaviour as x tends to infinity. If:

we can say that M(x) grows slower than x², whilst if:

we can say that M(x) grows faster than x². In the eventuality that:

we say that M(x) grows like x², regardless of what finite value the limit takes – simply multiplying or dividing M(x) by a constant can make this limit equal to 1, meaning that the two functions are tending towards each other, which equates to them growing at the same rate.

Usefully, Mandelbrot has established that the growth rate of this function maps directly to the rate of decay of the right-hand tail of their corresponding Complimentary Cumulative Distribution Function (or Survival Function). Given a random variable X's Probability Density Function φ(x), its Cumulative Distribution Function is given by:

Its Survival Function is then:

Mandelbrot's insight is the following:

• If, as per Borderline Mild Randomness,

  Therefore the Exponential Distribution is necessarily a Borderline Mild distribution.

• If, as per Delocalised Slow Randomness,

  This is a family of functions that decay more slowly than e⁻ˣ.

• If, as per Localised Slow Randomness,

  This family of functions decays slower still.

• If, as per Pre-Wild Randomness,

  This means that the tails of the Probability Density Function φ(x) will decay like x⁻ᵅ⁻ᣳ. Notably, the previous state’s decay rate of

  stipulated that m>1, because when we allow m=1 this simplifies to

  As long as m>1, this family of functions decays faster than a power law, whereas a Pre-Wild distribution’s Survival Function's tail will decay as a power law (where the power is greater than 2).

• By allowing for the second moment to become infinite as well, Wild Randomness is the domain of distributions whose Survival Function's tails decay like x⁻ᵅ, and whose Probability Density Function's tails decay like x⁻ᵅ⁻ᣳ for α≤2.

• Mandelbrot writes that Extreme Randomness is something that he “never encountered in practice”. The fact that such a distribution would not even have fractional moments is equivalent to the statement that its Survival Function decays slower than any power law, even fractional powers. This means that it must decay logarithmically.

After all of that, it is still difficult to gain an intuition about these states. The heuristic of even and concentrated portioning provides a basis for the original 3 states of Mild, Slow and Wild, but even then, if you are given the formula for a distribution, it is not obvious how you might go about classifying it. My aim is to come up with a way to more easily visualise how each of these classes of distributions behaves. Importantly, what I am doing below is not going to be a mathematical proof – it may well be provable, and the methodology below may suggest an approach, but I am only seeking to expound a heuristic here.

V. Compression

Given a particular distribution, it would be useful to be able to apply a transform to it that would bring the tails that disappear off towards infinity into a finite realm where they can be inspected. The idea here is to effectively “compress” the tails of the distribution into a finite interval in some sort of consistent way so that different distributions can be compared. Firstly, to keep things consistent and straightforward I will only use distributions that are either defined over the domain (0, ∞), or that are symmetric about 0 and defined over the domain (-∞,∞). The next thing to do is to ensure that the area under this new compressed curve is still 1, as was the case with the distribution itself beforehand.

One way to do this, is to find a function g(x) that maps between the interval (-∞, ∞) and a finite interval. The hyperbolic tangent (or tanh) is one such function, mapping from (-∞, ∞) to (-1, 1), however ideally we want a function the other way around, that takes in values from -1 to 1, and can output any real number. For this, we can simply use the hyperbolic tangent’s inverse function, referred to as arctanh(x) or tanh⁻ᣳ(x).

Because the output of arctanh(x) is a number in the interval (-∞, ∞), we can feed this number into our probability density function f(x). These two functions combined are then f(g(x)) so if g(x) = arctanh(x), this give us f(arctanh(x)). This is a transformed version of the probability density function fitting within (-1, 1) on the x-axis – very close to what we wanted. Below is a plot of the Gaussian Distribution (with mean 0 and variance 1) transformed in such a way:

This looks like it is doing what we want, but there is a little housekeeping left to do.

Firstly, we don’t want distributions with the same tail properties but different scales to behave differently under this transformation. For instance, this transform would look different if we used a Gaussian Distribution with variance 2 rather than 1, even though the choice of variance doesn’t change the tail behaviour. This also cannot be dealt with by simply adjusting for the variance of the distribution, as distributions classed as “Wild” do not have a well-defined variance. We can however use the median of right-handed distributions, and the third quartile of symmetric distributions. Keeping zero mapping to zero, we can map the median of a right handed distribution defined on x∈[0, ∞) to 0.5, and we can map the third quartile of a distribution symmetric about 0 to 0.5 (effectively mapping to 0.5 the median of the part of the distribution defined on [0, ∞), which keeps both types consistent). This means that we want to adjust the transformation to make

which would then neatly split the transformed graph into 4 vertical sections of equal width (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1) corresponding to the intervals on the untransformed distribution of the four quartiles (or above and below the median for right-handed distributions). For g(x)=arctanh(x), we find that

so we can simply rearrange this equation to give

This suggests that we should use

going forwards, or for a more general function g(x), we want to look at the transformation:

Secondly, the area under this graph is clearly not 1, so we need to adjust the transformation to make it preserve the area. This turns out to be very easily doable by an application of the chain rule – we know that

and for any function g(x), the chain rule gives us

This means that our transformation simply needs to be multiplied by the derivative of

and it will meet our requirements. The expression

is a constant with respect to x, and can therefore be taken outside the derivative if necessary, so we can refer to this transformation as:

This is still a very easy to apply transformation and we can see how it treats the Gaussian Distribution now that it has been adjusted to renormalize horizontal scaling and preserve the area under the curve.

The Gaussian Distribution (mean 0, variance 1), given by the probability density function

is shown on the two graphs below, before and after transformation:

The Gaussian Distribution with mean 0 and variance 1 has its third quartile at 0.67449, you have:

With this, you can easily reproduce the second plot by typing the following into Wolfram Alpha:

plot 1/sqrt(2π) e^(-g^2/2) dg/dx substitute g=0.67449 arctanh(x)/arctanh(0.5) from x=-1..1 y=0..0.6

Importantly, this function is still 0 at x=1 and x=-1. Furthermore, as the area under the graph has been preserved by the transformation, the area under the curve between say x=0.99 and x=1 is the same as the area under the original un-transformed probability density function between

or more generally:

It can also be verified that using a Gaussian Distribution with a different variance gives the same result (e.g. variance of 4, which results in a third quartile at 1.34898).

In terms of Mandelbrot’s seven states, the Gaussian Distribution falls into the Mild class. The transformation’s behaviour at ±1 is fundamentally a statement about the tails, and the fact that they go to 0 under this transformation tells us that they decay at a certain rate. Whilst not yet a mathematically rigorous concept, it is easy to see how other distributions whose transformations also go to 0 at ±1 might decay at similar enough rates to be counted as Mild. Let’s look at how this transformation treats a few different distributions.

Generalised Gaussian Distribution with shape parameter 3 [before, after] - this distribution has even lighter tails than the Gaussian Distribution, which is reflected in the way that the "shoulders" of the second graph fall towards zero earlier than they did for the Gaussian Distribution:

Maxwell Distribution (also known as the Chi Distribution with 3 degrees of freedom) [before, after]:

Rayleigh Distribution with scale parameter 1 (also known as the Chi Distribution with 2 degrees of freedom) [before, after] - note again that a different scale parameter results in the same transformed graph - the Rayleigh Distribution with scale parameter 1/√2 (also known as the Weibull Distribution with shape parameter 2) has different mean and variance, but the transformation maps it to the same shape:

Chi-Squared Distribution with 6 degrees of freedom (also known as the Gamma Distribution with shape parameter 3 and scale parameter 2) [before, after] - again, a Gamma Distribution with shape parameter 3 and scale parameter 1/3 is mapped to the same shape:

Chi-Squared Distribution with 3 degrees of freedom (also known as the Gamma Distribution with shape parameter 1.5 and scale parameter 2) [before, after]:

All of the above distributions are in the Mild category, and conveniently all go to zero at x=1 (even the last one - it is just such a steep curve that Wolfram Alpha doesn't plot it).

VI. The Borderline

What happens when we try a few Borderline Mild distributions?

Exponential Distribution, scale ½ (also Gamma Distribution, shape 1, scale 2; Weibull Distribution, shape 1 scale 2; Chi Squared Distribution, 2 degrees of freedom) [before, after]:

Chi-Squared Distribution, 1 degree of freedom (also Gamma Distribution, shape 0.5, scale 2) [before, after]:

Laplace Distribution (also known as Generalised Gaussian Distribution with shape parameter 1) [before, after] - this distribution is a scaled exponential distribution reflected about the y-axis:

Logistic Distribution [before, after]:

None of these distributions go to zero at x=1, which is again very convenient. Their curves either go to some finite value or shoot off to infinity as x tends towards 1. As a heuristic, this gives us a good measure for when something is Mild – if this transformation goes to zero at x=1, it is Mild, otherwise it is Borderline Mild or worse. As an aside, this transformation for the Logistic Distribution is interesting because it is a straight line. This is a direct consequence of the fact that the cumulative distribution function for the Logistic Distribution is itself a scaled hyperbolic tangent function

where s is the scale parameter. We can prove that this is in fact exactly a straight line as follows:

Going forwards, as shorthand I shall refer to a transformation taking a distribution to zero at x=1 as the transformation having “tamed” the distribution. As the above transformations have not tamed these Borderline Mild distributions, they are not going to tame any distributions that are in a higher state of randomness either. The question therefore is, how do we tell the difference between all the other states of randomness?

VII. Transformation Family

The function we have used so far g(x)=arctanh(x) is only one of many inverse-sigmoid curves that would serve a similar purpose of compressing the domain (-∞, ∞) down to (-1, 1). We can construct a whole range of different transformations for different functions g(x) that are of the form:

The most fundamental properties that g(x) must have, are that it is continuous, monotonically increasing, asymptotic at x=±1, and that g(x)=-g(-x). Beyond this though, if we are looking to discern different tail behaviours, we need different functions g(x) that are asymptotic at different speeds. For a function that tends to infinity at x=1, arctanh(x) tends to infinity exceedingly slowly. Putting some numbers in, we get arctanh(0.99)=2.65, arctanh(0.9999)=4.95, arctanh(0.999999)=7.25. Every time we get 100 times closer to 1, we still only go up by around 2, so in order to compress the tails of heavier tailed distributions more, what we need is a function that gets there faster.

We can construct a faster growing function by multiplying g(x) by a function that is symmetric about the origin and increases as it gets closer to ±1. We don’t need to worry too much about what values it actually takes as long as it is positive and non-zero, as the transformation uses the constant k to ensure that it will scale the whole thing appropriately, mapping g(1/2) to the value that is the median of the positive half of the distribution. Let’s start with 1+x², as the slowest growing symmetrical polynomial:

We can of course multiply it by this again and again, building up a whole family of transformations, each growing faster than the last:

But there is still further that we can go; (1+x²)ⁿ is not asymptotic, so the function arctanh(x) grows faster than it. We can make something symmetric and non-zero by taking:

We can therefore multiply g₀(x) by this to get another family of transformations, again each growing faster than the last, with the first one ultimately growing faster than any in the previous list:

This is still not the fastest g(x) we can find though – the reciprocal of any polynomial will grow faster than any power of arctanh(x), so we can take the non-zero symmetric function:

and multiply it by x to get another inverse-sigmoid curve that grows faster than any of the above, then keep multiplying it by the symmetric function for another list (please excuse the slightly odd choice of subscripts - it is done to avoid confusion later):

Finally, we can construct yet another that will grow faster than any of these (it would of course be possible to construct yet faster ones, but this will suffice for our purposes here):

Armed with this array of transformations, we can return to looking at some more heavy tailed distributions.

VIII. The Wilderness

In his book “Fractals and Scaling in Finance”, Mandelbrot mentions that the Slow states of randomness (Borderline Mild, Slow Delocalised, Slow Localised and Pre-Wild) are more subtle to deal with, and I quite agree. As such, I shall start looking at the Wild states first. To remind ourselves; Wild Randomness occurs when even the 2nd moment is infinite, so the variance is not defined. There exists some moment (possibly fractional) μₘ, m>0 that is still finite, and Long-run Portioning is concentrated for all N.

In fact, I am inclined to draw a further distinction between the states of randomness for which Long-run Portioning is concentrated for all N (those being Wild and Extreme according to Mandelbrot). The Wild category as defined by Mandelbrot has a natural dividing line at the point where the 1st moment ceases to be defined – splitting the category into those distributions with a mean, and those whose mean is also undefined. It is undeniable that a distribution whose mean is undefined is significantly more pathological than one which has a mean, so it makes sense to split these out. If you are sampling from a distribution whose mean is undefined and you try to take the mean of your sample, you can calculate it, but as you take more samples the sample mean you are calculating will never converge to a value – the samples you take will occasionally be so vast that it will shift the mean significantly in a random direction, no matter how many samples you have already taken.

If we continue to refer to the state of randomness with undefined variance but valid mean as Wild Randomness, we can refer to the state with undefined mean but some valid fractional moment as Aggressively Wild randomness, or perhaps Aggressive randomness for short. It is worth noting that this Aggressive state is different from the Extreme state, for which not even fractional moments exist. I have seen it written or implied occasionally that the Extreme category includes anything which has an undefined 1st moment, but this is incorrect as per Mandelbrot’s original framing of the states.

When he says that he never encountered Extreme randomness in practice, he wasn’t forgetting things like the Cauchy Distribution and the Lévy Distribution, both of which are relatively well known distributions with an undefined mean. Unlike genuinely Extreme randomness however, they do have fractional moments, for example the ¼ᵗʰ moment of the Lévy Distribution is:

I shall refer to this category as Aggressive, to set them apart from both the Wild and the Extreme, but make no mistake – the state of Extreme randomness really is not inappropriately named – by not even having fractional moments that are defined, no matter how tiny, they really are teetering on the boundary of being valid probability distributions at all.

Initially, let’s restrict ourselves to the Wild category (by which I mean not the Aggressive category). To start with, let’s see what happens when we use

for our transformation – we can apply these to a few different distributions to get the idea.

Student’s T Distribution, 2 degrees of freedom [before, transform 1, transform 2]:

Arcsinh-Logistic Distribution, shape parameter 2 (this is the distribution of a random variable, the inverse hyperbolic sine of which is distributed like a Logistic Distribution with scale parameter 2) [before, transform 1, transform 2]:

Pareto Distribution, shape parameter 2 [before, transform 1, transform 2]:

Fisk Distribution, shape parameter 1.5 (also Log-Logistic Distribution shape 1.5 – this is the distribution of a random variable, the logarithm of which is distributed like a Logistic Distribution with scale parameter 1.5) [before, transform 1, transform 2]:

Inverse-Chi-Squared Distribution, 3 degrees of freedom (also Inverse-Gamma Distribution, shape 1.5, scale 0.5) [before, transform 1, transform 2]:

We can see from all of these, that the

transformation does not tame them, but

does.

IX. Getting More Aggressive

We can now see whether the state of Aggressive randomness behaves differently (spoilers – it does). Let’s use:

to assess these, and where neither of them successfully tame the distribution, we can try:

as well.

Slash Distribution [before, transform 1, transform 2]:

Cauchy Distribution (also Student’s T Distribution, 1 degree of freedom; Stable Distribution, stability parameter 1, skewness parameter 0) [before, transform 1, transform 2]:

Arcsinh-Logistic Distribution, shape parameter 1 [before, transform 1, transform 2]:

Student’s T Distribution, 0.5 degrees of freedom [before, transform 1, transform 2, transform 3]:

Pareto Distribution, shape parameter 1 (also Fisk Distribution, shape 1; Log-Logistic Distribution, shape 1) [before, transform 1, transform 2]:

Lévy Distribution (also Inverse-Chi-Squared Distribution, 1 degree of freedom; Inverse-Gamma Distribution, shape 0.5, scale 0.5; Stable Distribution, stability parameter 0.5, skewness parameter 1) [before, transform 1, transform 2, transform 3]:

We can see that

no longer tames these distributions, but

tames some of them, and

tames them all. In fact, for any distribution in this category, there should be some

that does the job. We can observe that a distribution resembling a power law with an exponent k will be tamed by

for example the Pareto Distribution with shape parameter 0.5 has a term like

and is tamed by

As the exponent k in a power law can be arbitrarily close to 1, the power required to tame an Aggressive distribution could be arbitrarily high. This is fine though, as because

grows faster than all of them, it should tame any distribution that is aggressive.

Now we just need to make sure that Extreme distributions behave yet differently, to make sure that we can tell the difference using these transformations. We can use

again, to see what happens.

Arcsinh-Cauchy Distribution (this is the distribution of a random variable, the inverse hyperbolic sine of which is distributed like a Cauchy Distribution) [before, after]:

Log-Cauchy Distribution (this is the distribution of a random variable, the logarithm of which is distributed like a Cauchy Distribution) [before, after]:

Unlike the Aggressive distributions, these Extreme distributions are not tamed by this transformation, which is useful as it allows us to distinguish between the different categories.

X. The Liquids of Randomness

We have now picked the low hanging fruit. Rather poetically, Mandelbrot likens the states of randomness to the states of matter – Solid, Liquid and Gas compared with Mild, Slow and Wild. Mild randomness behaves metaphorically like a solid – unsurprising and inert – the extremes in your data/model won’t really be extreme at all. Wild randomness (encompassing Wild, Aggressive and Extreme) behaves like a gas – all over the place, but obeying its own rules that make sense – extremes are the defining feature of your data/model. Slow randomness (encompassing Borderline Mild, Slow Delocalised, Slow Localised and Pre-Wild) he compares with a liquid – a strange mixture of both behaviours, sometimes acting in ways that a solid might (falling from a height, water is as unforgiving as concrete/with enough data, you find that the extremes are effectively bounded), but other times behaving similar to a gas (liquids get everywhere/with a small enough sample, the extremes dominate enough to skew the data). It is clear from this, that Mandelbrot considers Slow randomness to be tricky to deal with.

We have already established the boundaries of Slow randomness (again – heuristically, not by proof). We know that g₀(x)=arctanh(x) is insufficient to tame Borderline Mild distributions, and by virtue of Wild distributions being tamed by

we can assume that Pre-Wild distributions will be tamed by

This means that anything that is not tamed by g₀(x)=arctanh(x), but is tamed by

should be Slow randomness, but that spans four of Mandelbrot’s states, so it would be useful if we could be more specific.

Thankfully, in between these two functions, we have already established that there are a couple of families of functions that may be instructive:

In fact, we can eke out a third (which will hopefully slightly justify the slightly contrived choice of subscript earlier), by noting that we can take the third family

and extend it in the other direction, starting with:

No matter how large n becomes, there will be a point after which

These three families are exactly what we need, but the words “there will be a point after which” already indicate where the problem lies. We can construct transformations that might theoretically discern between the types of slow randomness, but the behaviour that we are interested in (what happens at x=1) may cease to be obvious. Let’s try anyway and see what goes wrong.

Having just dealt with the Wild category, we can start with the distributions exhibiting Pre-Wild randomness. Many of these look like power laws, similar to the Wild distributions that were tamed by

so the obvious thing to try is

For simplicity, we can use

Student’s T Distribution, 5 degrees of freedom [before, transform 1, transform 2, transform 3]:

Student’s T Distribution, 3 degrees of freedom [before, transform 1, transform 2, transform 3]:

Pareto Distribution, shape 7 [before, transform 1, transform 2, transform 3]:

Fisk Distribution, shape 3 (also Log-Logistic Distribution, shape 3) [before, transform 1, transform 2, transform 3]:

Inverse-Chi-Squared Distribution, 5 degrees of freedom (also Inverse-Gamma Distribution, shape 2.5, scale 0.5) [before, transform 1, transform 2, transform 3]:

In a similar manner to the Aggressive category, we can suggest a fairly sensible rule of thumb. It looks like a Probability Density Function that behaves like 1/xᵏ (which implies a Survival Function that behaves like 1/xᵏ⁻ᣳ) will be tamed by

for example the Pareto Distribution with shape parameter 10 has a term like 1/x¹¹ and is tamed by

This appears to be related to the largest moment that is defined for these distributions – for a distribution whose Probability Density Function resembles a power law with exponent m, the largest moment that is defined will be μₘ₋₂ (again, for example, the Student’s T Distribution with 4 degrees of freedom has a Probability Density Function that behaves like 1/x⁵ and has a defined skewness (μ₃) but undefined kurtosis (μ₄), fitting this trend).

The issue with this, is that although we have that a Pre-Wild distribution will be tamed by

and there will be some n for which it is not tamed by

this n could be arbitrarily large. We cannot exhaustively search through to find the n at which the transformation ceases to tame the distribution. Therefore, unless we come across one that does fail to tame it, we can’t be sure that the distribution isn’t in a different category of Slow randomness.

Skipping to the other end of the spectrum of Slow randomness, we can look at distributions that we know are Borderline Mild (the same ones as in the borderline section). We can hypothesise that they will be tamed by

for some n, and therefore that

will tame all of them as well. We can apply

to see the effect:

Logistic Distribution [before, transform 1, transform 2, transform 3]:

Exponential Distribution [before, transform 1, transform 2, transform 3]:

Exponential-Logarithmic Distribution, shape 0.5, scale 1 [before, transform 1, transform 2, transform 3]:

Chi-Squared Distribution with 1 degree of freedom [before, transform 1, transform 2, transform 3]:

With the Chi-Squared Distribution with 1 degree of freedom, it becomes apparent what the problem is. As per Mandelbrot, all Gamma Distributions with shape parameter ≤1 are Borderline Mild, so if the hypothesis is correct, we will still need higher and higher powers of (1+x²) to tame the function as the shape parameter gets smaller. There is no limit to how high this power might need to be. The effect of

however is equally unhelpful – we can see that as the shape parameter gets smaller, even though it is always zero at x=1, it can spike arbitrarily high just before 1, giving the illusion that it is not going to zero after all.

We can similarly hypothesise that Slow Delocalised randomness is tamed by

for some n, but this has similar problems. We can apply

to see:

Generalised Gaussian Distribution, shape ½ [before, transform 1, transform 2]:

Generalised Gaussian Distribution, shape ¼ [before, transform 1, transform 2]:

Weibull Distribution, shape ½ [before, transform 1, transform 2]:

Generalised Exponential Distribution, shape ¼ [before, transform 1, transform 2]:

Here we have the opposite problem – distributions that look like they are going to zero under g₈(x), but that actually shoot off to infinity at the last moment – a problem that gets worse with gₙ(x) as n increases. Clearly, even if these two hypotheses are true, it is not necessarily reliable for easily distinguishing between Borderline Mild and Slow Delocalised, as the behaviour at x=1-ε may not be indicative of whether the transformation goes to zero at x=1 or not.

We are left with the Slow Localised category, which is epitomised by the Lognormal Distribution. The Lognormal is very commonly used in a lot of analysis, because its straightforward relation to the Gaussian Distribution makes it very easy to work with. Mandelbrot however, really doesn’t like the Lognormal Distribution – in fact he devotes an entire chapter of his book to why its overuse is so problematic. He states:

“It is beloved because it passes as mild: moments are easy to calculate and it is easy to take for granted that they play the same role as for the Gaussian. But they do not. They hide the difficulties due to skewness and long-tailedness behind limits that are overly sensitive and overly slowly attained”

“This distribution should be avoided. A major reason… is that a near-lognormal’s population moments are overly sensitive to departures from exact lognormalities. A second major reason… is that the sample moments are not to be trusted, because the sequential sample moments oscillate with sample size in erratic and unmanageable manner.”

It is this category then, that we are left with, having no easy families of transformations left to try. These distributions should have tails that are eventually heavier than any Slow Delocalised distribution, but lighter than any Pre-Wild distribution. This means, that if the above heuristics are correct, they should not be tamed by any transformation using

but should be tamed by every transformation using

Of course, the issues we established with the Borderline Mild and Slow Delocalised distributions are very much relevant here. The heuristic may have been somewhat informative for the other categories of Slow randomness – allowing positive identification of many distributions that don’t require us to delve too deeply into any of the infinite families of transformations, and whose transforms don’t have behaviour at x=1-ε that is too pathologically different to their behaviour at x=1. Unfortunately, the Slow Localised category falls right into the middle of the gap between two of the infinite families of transformations, which renders the heuristic unable to determine whether the distribution is truly Slow Localised, or if it is just a particularly badly behaved Slow Delocalised or Pre-Wild distribution. In fact, if we try to use the transformations

on a couple of Slow Localised distributions, we get very odd results. The additional two graphs show the same transforms, but zoomed in very close to x=1:

Lognormal Distribution [before, transform 1, transform 2]:

Arcsinh-Gaussian Distribution [before, transform 1, transform 2]:

We can see that the graphs look the wrong way around – the distributions look like they are

which should not be possible. It is only when we zoom in incredibly far, that we see that the opposite is in fact true.

If we tried with transforms based on

this would only get worse - requiring zooming in even further (potentially further than is actually possible using Wolfram Alpha).

XI. Stability

Having trawled through all of the States of Randomness, it is worth noting a very important property of Wild, Aggressive and Extreme randomness - they no longer obey the classical Central Limit Theorem.

The Central Limit Theorem states that if you add n i.i.d (independent and identically distributed) random variables together, the sum of the variables will tend towards being distributed according to a Gaussian Distribution as n→∞. This however only applys when these random variables are distributed according to a distribution with finite variance (which means either a Mild or a Slow distribution).

If you have i.i.d. random variables that are distributed according to a Probability Density Function with tails that decay like x⁻ᵅ⁻ᣳ (or equivalently a Survival Function that decays like x⁻ᵅ, also known as "Paretian Tails"), the Generalised Central Limit Theorem states that for 0<α≤2 (Wild and Aggressive randomness), this sum will tend towards being distributed according to a "Stable Distribution" with "stability parameter" α.

These Stable Distributions have the same kind of Paretian tails as the distributions that generated them, so for example, the sum of n random variables that were generated by a Student's T Distribution with 1.5 degrees of freedom will tend towards being distributed according to a Stable Distribution with stability parameter 1.5 as n→∞. It is for this reason that Mandelbrot refers to Wild randomness as "Tail Preserving".

The stability parameter that defines the family of Stable Distributions can vary between 0<α≤2, and the Stable Distribution with stability parameter 2 is the Gaussian Distribution. This has several implications:

• Pre-Wild randomness (Paretian tails with α>2) falls under the classical Central Limit Theorem, so under these conditions all will tend towards the Stable Distribution with stability parameter 2 (the Gaussian Distribution)

• Wild randomness with α=2 (e.g. Student's T Distribution with 2 degrees of freedom, Fisk Distribution with shape parameter 2, Pareto Distribution with shape parameter 2 and Inverse-Chi-Squared distribution with 4 degrees of freedom) will actually still tend towards the Gaussian Distribution in this limit, however for any finite sum of n random variables, the sum's distribution will still have undefined variance.

• Wild randomness with 1<α<2 and Aggressive randomness 0<α≤1 will tend towards a non-Gaussian, heavy tailed Stable Distribution with stability parameter =α in this limit.

• Extreme randomness is still not covered by this theorem, as Extreme distributions have tails that are even heavier than Paretian tails. These are rarely used distributions, but it does not appear to be known what their behaviour is in this limit.

Most Stable Distributions have Probability Density Functions that are not expressable in terms of elementary functions, which makes them rather hard to deal with (with the exception of the Gaussian, Cauchy and Levy distributions). Their stability under summation of random variables was a key feature that Mandelbrot was interested in however, due to his focus on fractals and self-similarity. If you have a stochastic process whose evolution over time is self-similar (for instance its movements over a day are indistinguishable from its movements over a year), which he hypothesised was the case for the stock market and commodity prices, you have a situation where the sum of multiple random variables (daily movements) must behave the same as the individual random variables themselves (minute by minute movements). In other words, random variables distributed according to a Stable Distribution.

XII. Conclusion

At this point, it is natural to ask what has been achieved by all of this. The claims above are not rigorously proven, therefore the transformation discussed is only a heuristic. Hopefully however, it provides a useful lens with which to view the tail behaviour of various distributions, giving more of an intuitive feel of how different heavy behave.

Whilst Mandelbrot’s book originates the concept, it is first and foremost an academic text from someone at the forefront of a field of study, which makes it unsurprisingly dense and impenetrable. It provides the basis for the taxonomy he developed, but is remarkably short on examples, which are often a good way to gain understanding of a topic. He did write another book aimed at a more general audience, that is much more accessible and gets across some of his ideas in this area. I highly recommend reading it, but unfortunately one thing that it doesn’t go into much detail on, is this taxonomy for classifying randomness.

Dealing with heavy tails is an area of probability that is hugely important for understanding real-world processes, and the tendency for people to try to shoe-horn their data into Gaussian or Lognormal models is likely due to the underdevelopment of tools for dealing with these other types of randomness. As such, I hope that the plethora of examples above is able to make the concepts slightly more accessible and encourage further exploration.

In summary, assuming that the behaviour of the transformation

is as described, we can add it to the descriptions of the different states of randomness that were listed earlier. This gives us the following:

• Proper Mild Randomness

  • Short-run Portioning is even for N=2

• Borderline Mild Randomness

  • Short-run Portioning is concentrated

  • Long-run Portioning becomes even, for some finite N

  • The n^th root of the n^th moment grows like n

  • Right-hand tail of the Survival Function decays like e⁻ˣ

• Delocalised Slow Randomness

  • The n^th root of the n^th moment grows like a power of n

  • For some m>1, right-hand tail of the Survival Function decays like

• Localised Slow Randomness

  • The n^th root of the n^th moment grows faster than any power of n

  • All moments still finite

  • For some m>1, right-hand tail of the Survival Function decays like

• Pre-wild Randomness

  • Moments grow so fast that some higher moments are infinite

  • The 2^nd moment (variance) is still finite

  • Long-run Portioning still becomes even, for a large enough finite N

  • Right-hand tail of the Survival Function decays like x⁻ᵅ for some α>2

• Wild Randomness

  • Even the 2^nd moment is infinite, so the variance is not defined

  • The 1st moment (mean) is still finite

  • Long-run Portioning is concentrated for all N

  • Right-hand tail of the Survival Function decays like x⁻ᵅ for some 1<α≤2

• Aggressive Randomness

  • Even the 1^st moment is undefined There exists some moment (possibly fractional) μₘ, m>0 that is still finite

  • Right-hand tail of the Survival Function decays like x⁻ᵅ for some 0<α≤1

• Extreme Randomness

  • All moments μₘ, m>0 are infinite

The pursuit of happiness is something of a universal human endeavour. As such, one could consider it odd that we are so divided about how to achieve happiness - after all, it is something we have been trying to reach as a society since time immemorial.  Unfortunately this view neglects the fact that the pursuit of happiness is such a significant motivator for people, that there are an enormous number of people and organisations out there trying to convince people that their method is the one, in order to gain influence, profit or status.  In this environment, it is difficult to filter the noise and disinformation from the genuine signal of how to live a happy life.

This being the case, it is quite natural to look for ulterior motives behind anyone discussing happiness and ways to achieve it, in case they are selling something, or trying to recruit you into a cult.  Nevertheless, I intend to share my musings on the subject.

Philosophical discussions of happiness often touch upon ideas such as “wire-heading” or drug induced euphoria, but to many this sounds unappealing - it is not desirable to become a “happiness robot”.  To remain identifiably human, it seems necessary to still be able to be affected by things happening around you, including the bad - we want to minimise the bad things that happen, not stop caring that bad things are happening.  This gives us two lines of attack - one being reducing the amount of bad things that happen, and the other being improving your baseline happiness. It is the second of these that I am considering here.

In seeking to have a high baseline of happiness, we are not trying to be unaffected by negative things - just to be consistently happier on average.  Sad things will still happen, and we will still care about these and seek to prevent them, but we want to be generally happy, rather than generally mediocre.  Improving baseline happiness is difficult, because our happiness levels tend to renormalise to the level they were at before. Whenever something good happens, we experience a spike in happiness, but this soon dies away, leaving us back feeling mediocre.  This may be why so many people end up with a sense of ennui, fed up with constantly chasing the highs of happiness, only for it not to last.

I am inclined to think however that this renormalisation is not quite so inevitable.  If you are aware of it, you can do things to counteract it. This does take effort, but relatively little considering the pay-off.  Finding things to be happy about - consciously thinking about things that are good about your life, rather than taking them for granted (“appreciating the simple things in life”) is a very powerful way to give yourself a happiness boost.  If you can make a habit out of this, it is possible that without buying anything or joining any cults, you could consistently improve your baseline happiness.

The blog Putanumonit has an excellent post on how to be more mindful of what actually makes you happy.  One of the main messages in this post is something fairly similar - time spent thinking about good things makes you happy - have good experiences, and remember to think about them.  Further to this concept, I would add - if you have bad experiences, find aspects to them that were positive, and focus on those (“character building”). If there is no way to find any positive aspect, and the experience was just too traumatic, it is probably best to try not to dwell on it, and form other better memories to think about instead.  Another key message from this post is not to try to remove all variation - if you “treat yourself”, this will give you a happiness boost, but if you turn a treat into something you do all the time, the boost will not be sustained, and will be normalised away.

There is also an excellent CGP Grey video describing all of the things not to do if you want to be happy.  If someone were doing any of the things listed here, stopping doing them would be a pretty sure-fire way to improve their baseline of happiness.

This idea of improving the baseline could be challenged by claiming that people with a lower baseline might be more motivated to solve the world’s problems, which would make people happier in the long run however I don’t think that is the case at all.  As mentioned above, the aim of having a higher baseline is not to stop feeling sad when sad things happen, so people should still be motivated to improve the world. In fact, despair and despondency are demonstrably huge demotivational factors, so it is likely that someone with a higher baseline happiness will be more hopeful, and more willing to try to make the world a better place.

Stoicism & Epicureanism

Splitting the discussion of happiness in two, between a discussion about the baseline and a separate discussion about making the world a better place, matches very well with the two competing greek philosophies of Stoicism and Epicureanism.

Stoicism, put extremely simply, is based around the goal of being happy with what you have - considering the positives of the situation you find yourself in, and finding comfort in the fact that your life is not worse.  It is a very grounded philosophy, not seeking any dizzying pleasure, but aiming to give people a toolkit with which to deal with adversity and tragedy. It has however often been accused of callousness, as when applied too broadly to other people rather than oneself, it suggests that everyone should be more accepting of their lot in life - if someone cannot find something to be happy about, they are simply not being stoic enough.

Epicureanism is the historical opponent of stoicism, and as such, unsurprisingly takes a fairly opposite approach.  The goal of Epicureanism is to derive the greatest amount of pleasure possible during one’s lifetime. To many people this may be a much more natural way to pursue happiness, but it has in turn often been accused of promoting hedonism and decadence.  (The criticisms of both Stoicism and Epicureanism are quite unfair, and do not do justice to the original, highly nuanced philosophies espoused respectively by Zeno and Epicurus themselves, however they are easy complaints to have against the much simplified concepts that they are often portrayed as today.)

I would argue however that these two philosophies are not so incompatible as it would at first appear.  The strength of Stoicism is in its application to one’s personal situation - giving people the tools to improve their baseline happiness; and its weakness is when it is too simplistically applied to society and used as a stick to beat people with for being insufficiently grateful for their lot in life.  The strength of Epicureanism on the contrary is in its application to society - improving the world we live in, to facilitate greater enjoyment and happiness for all; while its weakness is when it is too simplistically applied to an individual, promoting hedonism and selfishness. These strengths and weaknesses complement each other very well, suggesting a promising hybrid philosophy of personally applied Stoicism, but societally applied Epicureanism. 

Put more clearly, these strengths and weaknesses can be described like this:

Stoicism

• Personally applied is good - appreciating and making the best of what you do have, without dwelling too much on any negatives, developing resilience and positive thinking.

• Societally applied is bad - each to their own, people should just get on with it and accept their lot in life because complaining about things shows a lack of personal responsibility.

Epicureanism

• Personally applied is bad - pursuing the next happiness “high” without appreciating what you already have, failing to develop resilience to adversity, feeling like society owes you something.

• Societally applied is good - help others, be sympathetic to their needs, try to improve society to reduce the amount of adversity that people need to overcome.

It is hopefully not too much of a stretch to identify the parallels between “improving your baseline” and personal Stoicism, and between “improving the world” and societal Epicureanism.

The Free Energy Principle

There has been a fair bit of interest recently in the concept of the “Free Energy Principle” as introduced by the neuroscientist Karl Friston.  Scott Alexander has written about it at great length (archive), but the very simplified concept is the hypothesis that all of the actions our brains take are at a very low, subconscious level focused around trying to improve our predictions about the world we perceive.  This leads to framing concepts using a model of the brain as a probability estimation engine. A corollary of this, is that our moods might be a function of the statistical methods our brains are using to understand the world.  Again, Scott Alexander has explored this particular idea (archive), so I will attempt to summarise it very briefly.  If you have read this article, you may want to skip the next two paragraphs.

To summarise the concept of this theory of “computational mood”, it is proposed that there are two very important axes which determine your overall emotional outlook, over which your mind may vary.  These are firstly the expectation you have of outcomes in life, and secondly the amount of variance you expect in these outcomes. To put this more simply (but admittedly less accurately), this effectively boils down to firstly how positive or negative your outlook on life is, and secondly how sure you feel about what you expect to happen. These axes are usually plotted with the vertical axis corresponding to the expectation, with up being high expectation, and down being low.  The horizontal axis is then variance, with left being high variance and right being low (or perhaps more intuitively left being low confidence and right being high confidence in outcomes). 

If this theory is correct, there is probably a fairly healthy range in the middle, where most people’s minds reside quite comfortably, but taken to extremes, this allows us to proffer explanations for certain psychological issues.  If someone is in the far bottom-right, they have low expectations with high confidence - they have a negative outlook, and are very sure of it, which sounds a lot like depression. The far bottom-left by contrast characterises a negative outlook with high uncertainty - things will be bad, in some vague undetermined way, which sounds a lot like anxiety.  The far top-right is a very positive outlook with great certainty - the view that everything will be great, and will turn out perfectly, which sounds quite similar to mania.

The fourth quadrant - the top-left one, is one that has not yet been explored in academia. That is not to say that no-one has been thinking about it however - Jacob Falkovich has taken the concept of computational mood and attempted to generalise it far beyond its initial scope, paying specific attention to this quadrant.  I do not intend to go quite so far as Falkovich on this, but I hope to be able to draw a further parallel with the discussion above.

Relentless Positivity

Falkovich's article is excellent, and I must resist the temptation to quote entire paragraphs from it, so I shall limit myself to a couple of sentences:

“I spent a long time staring at that chart and then I realized – the top left is my corner. It’s where I’ve lived all my life.  Top left means that I’m very optimistic in general, but am quick to update to negative conclusions on the particulars.”

Falkovich does not put a name to this outlook, but I feel like I share it, and would describe it as “Relentless Positivity”.  Life may have its ups and downs, but if you inhabit this top-left space, you just roll with the punches, and push onwards. Here, I am not describing a person themselves as relentless - they are not obsessively pursuing a particular course of action, which might be more suggestive of overconfidence or mania - it is their positivity itself which is relentless.  Relentless Positivity to me suggests positivity that behaves in a way similar to The Terminator - dogged and unyielding, regardless of what obstacles are in the way. The top-left mood seems to embody the mental state of being able to be happy and see the positive, despite any setbacks, whilst still seeking improvement - neither blind confidence nor hopeless yearning.  This seems to be a pretty good fit for Relentless Positivity to me.

This mindset suggests the approach of “plan for the worst, expect the best”.  Accepting that outcomes may have significant variability is important, as this allows you to prepare for these eventualities.  Pessimism is expecting the worst to happen, whereas pragmatism is planning for the worst, whilst thinking positive, which stops people from giving up.  Another way to frame this mindset is to have an optimistic perspective on life, but a pessimistic approach to planning.

My feeling, is that this is good advice generally - plan for the worst, but find things to be happy about by noticing and appreciating the positive things in life.  It may come naturally to people that occupy the top-left mood of Relentless Positivity already, but it would be defeatist to suggest that other people could not follow these approaches, or that other people would not see benefits from using them.

Combining Old and New Perspectives

To tie this back to Stoicism and Epicureanism, we can view this vertical axis (high or low mean) as corresponding to personal approach - Epicurean or Stoic.  Epicurean implies dissatisfaction - an awareness that things could be better. Stoic implies making the best of what you have, finding ways to appreciate it. The horizontal axis (high or low variance) can then be viewed as corresponding to societal approach.  Epicurean implies an awareness of the world and the differences therein, allowing an awareness and expectation of a variety of results. Stoic implies an introspective approach, not attempting to make change or perceive differences, but to accept the status quo.

This implies that pure stoicism corresponds to mania.  This goes against our modern day use of the word stoic, which is often used to mean a kind of calm, emotionless fatalism - very much not our image of mania.  On the other hand, in a state of mania, people are usually convinced that everything is great, regardless of how the current situation looks objectively. In some sense, that is actually what Stoicism is trying to achieve, just without the excitement.  Therefore it could be viewed that mania is effectively “overshooting” the ideal of Stoicism, or is perhaps a failure mode of it.

Equally, this implies pure Epicureanism corresponds to anxiety.  This again goes against the idea of Epicureanism being the achievement of tranquility free from fear, but if we look at what it might mean to be a failure mode of this philosophy, we get somewhere.  Epicureanism seeks to satisfy pleasures without devolving into hedonism; to avoid pain without fearing it. At first glance this can seem contradictory, so it is not a stretch to imagine that someone trying to follow this philosophy might simply find new and inventive ways to be unhappy, whilst being stressed at their failure to make the formula work.

I feel at this point that the bottom-right quadrant - depression, is quite self explanatory.  Being societally stoic, will lead you to expect others to be accepting of their lot in life, not allowing for any expectation of change, but being personally epicurean will make you focus on any personal shortcomings or adverse events, seeing the negative without being able to find things to be positive about.

This identifies the top-left quadrant of Relentless Positivity with the proposed combination of being stoic about life - finding things to be personally happy about, and being Epicurean about society - finding ways to improve people’s happiness and planning how to avoid negative impacts on them.  This rather neatly ties together the idea of

Improve your baseline and improve the world

with the idea of

Plan for the worst, expect the best

Two very nice mottos that, whilst somewhat simplistic on the face of them, carry a great deal of meaning beneath the surface.

Intuitions about Real World Uncertainty

Uncertainty actually renders many philosophical gotchas irrelevant - the trolley problem variant in which pushing a fat man onto the tracks can save 5 people makes this obvious - there is no realistic world where one could be certain that this action would have the described effect, only different expected probabilities.  Our reaction to this question, to say that it seems wrong to push him is correct - even aside from the very human and visceral feeling of difference between flicking a switch and pushing someone to their death, we know instinctively that there is more uncertainty about whether it will stop the train, compared with switching tracks.  What if we push the man, and the others still die - we will have made the situation worse. At least when we are pushing a button to switch the train onto other tracks there is a very high probability that the switch will have the desired effect. We can insist when we phrase the question, that we are absolutely certain that the fat man’s body will stop the train, but this is simply impossible - we can never attribute a probability of 100% to anything, so the question simply becomes unrealistic.  The removal of uncertainty takes away a key feature of the scenario.

In general, it can reasonably be said that a large positive outcome that is justifying a negative action will always carry with it a risk that it is not guaranteed.  Performing the negative action could result in no positive outcome, so the positive must be discounted by a risk factor. This risk factor is then highly situational - it could be small, but in some situations it could be so large that it reverses the conclusion of the utility calculation.  This demonstrates very effectively why utilitarianism can often give nonsensical results in highly constrained situations. The scenario often demands that we know for “certain” the outcome of a particular action, which is impossible, and goes against one’s common sense. In the hypothetical world where the outcomes are all certain, the nonsensical result is correct, but only because the world is nonsensical too – absolute certainty can never be achieved, not least because there is always a non-zero probability that one is hallucinating, and the real world is not real after all.  This probability is usually small enough that it can be ignored within the calculation, but in a sufficiently contrived scenario, it becomes more likely, and can no longer be ignored.

Losing Your Sanity Has Non-Zero Probability

The concept of uncertainty can be applied to one’s own mental state.  It is possible to come up with many “traps” for utilitarians and consequentialists, in which you offer even higher stakes and more horrific acts than the aforementioned trolley problem.  Would you [commit extremely horrific/violent/traumatic act] against a [innocent bystander/child/loved one] in order to prevent the [the same horrific act being committed on a far greater scale/the death of all of humanity]?  (Please note, I have deliberately avoided specifics here, because I am aware that some people take these questions extremely seriously, and can experience psychological trauma through trying to wrestle with such questions about their own willingness or not to do these things.)  The point behind raising this, is that these situations are extremely contrived - if you think about one example, then consider the chain of events that would have to take place for you to end up having to make that choice, it is a highly unlikely series of events. I argue that it is far more likely that someone would be suffering from a mental illness such as a form of psychosis than that any such chain of events would occur to them.

This gives us a “get out of jail free card” for such questions - we may agree that technically the answer might be to do the [insert bad action here] in order to prevent the [insert even worse consequence], but we can state that in reality we would never do the [insert bad action here] because when faced with this choice, our uncertainty about our own mental state becomes relevant.  It is more likely that we are suffering from a form of psychosis that has convinced us that we have been presented with this choice, than that we have actually been presented with this choice in reality. This means that doing the [insert bad action here] would simply result in a world where a good person inexplicably has a psychotic break and does a terrible thing for no discernable reason.  This tells us that deontological injunctions are useful for utilitarians and consequentialists to avoid psychosis related issues. If what it would take for you to do [insert bad action here] is sufficiently contrived, it is reasonable to follow the rule “never do [insert bad action here], regardless of the circumstances” because the likelihood of you ever being in that situation is far lower than the likelihood of you ever getting a mental illness that warps your sense of reality, and your mind can make the stakes as high as it wants.

Further extending this, the question of what you would do in a “Groundhog Day” scenario becomes much clearer (where reality will reset itself, and the consequences of your actions will cease to exist).  Again the situation is extremely contrived - if you believe yourself to be in a state of reality in which there will be no persisting consequences, you are far more likely to be suffering from a mental illness.  Therefore the answer “no, I wouldn’t murder anyone” is completely reasonable, because if you ansewered any differently, you would be the kind of person that could be convinced to murder someone just because they thought they were in the plot of a movie.

When to Break the Rules

The effect of uncertainty also impacts the Law-Morality-Axiology hierarchy (archive).  The decision of whether your moral qualms are sufficient to override the law - finding the point at which the immorality of a situation overrides the negative societal impact of being seen to be eroding the legitimacy of the law, is a grey area riven with uncertainty.  Likewise the concept of “don’t let your morality get in the way of doing what is right,'' in which your consequentialist calculation suggests that in this particular situation, your normal moral rules are actually suggesting a harmful action - allowing yourself to break your own rules is a dangerous temptation to rationalise, but it is another uncertain grey area, as it can sometimes be for the best.  The boundaries of each of these are blurry, therefore there are choices between them that are permissible rather than mandatory.

Law and morality often suggest the same course of action, resulting in reasonably low uncertainty.  When morality starts suggesting a different course of action, uncertainty increases - there may be unintended consequences of breaking the law, or factors that you are not aware of or have not considered.  When faced with uncertainty, it is prudent to be conservative, sticking with the rule just in case. After a certain point however, the immorality of the law becomes less in doubt, and uncertainty starts to decrease again.  At this point it is not obvious whether to conservatively stick with the rule, or to follow what is moral. It only becomes clear that you should ignore the rule when uncertainty has decreased sufficiently - when it is blindingly obvious that the law is immoral, and needs to be changed, and the mere presence of that law is in itself eroding the legitimacy of the legal system.  The same applies when deciding whether to override morality with axiology - although we might prudently stick with our rules during high uncertainty, the area after the peak in uncertainty gives rise to a grey area in which it is permissible to override the rule, but not yet mandatory.

The Benefit of Prudence

This area of uncertainty is highly relevant to the concept of ethical offsetting - the idea that ethical decisions can be fungible, allowing us to do slightly unethical things, but apply effort in other areas to negate the effect.  Three key considerations contribute to this uncertainty:

1. Fungibility of outcome.  Taking an extreme example, allowing a person to kill someone, because it will save many lives, ignores the irreplaceability and non-fungibility of people. Without specific information about the people involved, the outcomes would need to be overwhelmingly skewed, before we could be sure enough of a positive outcome.

2. Risk of failure.  Even if people were fungible, and you decided to kill someone to harvest their organs, an organ donation might be rejected, thus not saving the recipient; the trolley problem examples which are instinctively more problematic such as “pushing the fat man”, are in part problematic because in reality the end results of the situations are much more uncertain. Invoking physically impossible levels of certainty that the trolley will be stopped does not convince the mind that the risk of failure has been removed.

3. Societal damage.  If, for example, wealthy people are allowed to break the law in too fundamental a way, due to having “offset” their transgressions, the rule of law itself could cease to be respected by wider society.  This would have huge negative impacts not initially factored into the offsetting calculation.

Again, we need to be well beyond the peak in uncertainty around any axiology-morality disagreement, in order to avoid other unconsidered negative externalities.  This then does potentially allow ethical offsetting in certain areas, but the outcome of doing “the axiologically better thing” must be adequately likely to be more positive than sticking with our moral code.

Personal Experience

[Trigger warning - injury, psychological trauma]

Going back to the idea that there is a non-zero probability that you are hallucinating, and that any consequentialist should acknowledge this in their assessment of a situation, I have a relevant personal anecdote.

The concept itself is one that I realised around a decade ago, when undertaking some very aggressive introspection. I had posed myself a hypothetical scenario, and was trying to work out what exactly it was, that made me so uncomfortable with the idea of committing a horrendous act in order to save all life on earth. It was not a pleasant train of thought, and I do not recommend such aggressive introspection to anyone (it is probably not great for your mental health). Once I realised why however, I was able to gradually incorporate "awareness of possible insanity" into my internal decision making apparatus. This may seem ridiculous, pointless or unreasonably abstract, but as luck would have it, this turned out to be far more beneficial than even I was expecting.

Just over four years ago, I was in a serious accident in which I broke... most things. The first few days in hospital I was sedated, but when I finally came around, I was extremely disoriented. The cocktail of painkillers that I was on at the time resulted in hallucinations, which exacerbated the disorientation and resulted in paranoia that I can best describe as a temporary Capgras delusion. I am fine now, both physically and mentally, but I still vividly remember how real the hallucinations felt while I was in this delusional state. I was convinced that the people I recognised around my bed were evil alien doppelgangers trying to lull me into a false sense of security so that they could experiment on me to find ways to enslave all of humanity. This sounds so obviously and completely ridiculous to any sane person, that it is almost laughable, but drug induced hallucinations can be really very convincing. Adrenaline coursed through my body as I realised that I had to escape at any cost - humanity depended on it.

Things could have gone very badly at this point. My body was still in a fairly precarious state, that would not have dealt well with a serious attempt at fight or flight. More than that though, the people around my bed who had been waiting for me to wake up were in an understandably fragile emotional state - it is quite scary to think how much psychological trauma I could have dished out if I had acted on my beliefs at that time without any reservations.

Thankfully, I did have reservations. Something in the back of my mind was already primed to consider the fact that I might not be entirely sane. This thought caused me to try to assess how likely it was that the situation was real, and despite my daze, I was able to conclude that at the very least the probability of alien abduction did not eclipse the probability that I was hallucinating. I was still highly suspicious of everyone, and fought against nurses trying to inject me with things, but I didn't say or do anything that couldn't be undone, just in case it wasn't real.