Epistemic status: so obviously wrong in hindsight that I’m a little embarassed.
Preface
If you clicked on the title of this post, then you definitely already know about Arrow’s impossibility theorem; but it has been my experience that many people, even those who are well-versed in the formal specifics of Arrow’s proof, miss many of its most important philosophical and practical upshots. I’ll leave the philosophy for another day (with only the hint that Kenneth Arrow is possibly the most important Hobbesian since Hobbes), and just talk about the practical.
The baby’s first explanation of the theorem is that Arrow proved that there is no perfect voting system. This first approximation is true as far as it goes, but also quite deeply incomplete. It leaves open the possibility that there is a best voting system: one that, while imperfect, is better than every alternative across a wide enough set of possible worlds. But, skipping over the technicalities, this is not true: the formal details of Arrow’s theorem (and Allan Gibbard’s extension of Arrow’s reasoning, sometimes given the lofty and unjustified title of “Gibbard’s theorem”) suggest that, in fact, different conditions demand different voting systems.1
For example, not only is there no voting system that can guarantee zero tactical voting, there is also no one system that minimises tactical voting across all possible situations. Or at least, there is no such system that also satisfies other very basic conditions, an observation that raises another point: there are many conditions we might hope for a system to achieve, that Arrow (and Gibbard) showed cannot even approximately be achieved simultaneously. This forces us to make trade-offs, and the question of how to resolve those trade-offs will depend on the particular circumstances policymakers find themselves in.
In other words, it is not just that there is no perfect voting system: there is not even an objectively least imperfect voting system. Everything depends on context. And while this fact is not often enough noted, it should be pretty intuitive: after all, common sense would suggest that the political culture of a nation, or its history, or its constitution, place demands and desiderata on voting systems that will not be the same everywhere. Which voting system a country should implement depends on contingent historical facts about society and politics in that country.
So, when thinking about voting reform for the UK—which should be high up on people’s agendas once more, now that it is the price for any future Labour–Lib Dem coalition—policies should be designed with the particular political conditions of the UK in mind.
The present conditions of the UK
The most important fact about the UK for designing electoral reform policy is this: Labour wins many urban seats by what can only be described as stupid margins. Consider Diane Abbott’s seat in Hackney, which she won in 2019 with a margin of over 33,000 votes. Thirty-three thousand! That’s nearly 60 percentage points. There are many Labour seats like this all over the country, especially in London and Liverpool but also in other major urban centres like Sheffield, Birmingham, and Manchester. As best as I can make out (correct me if I’m wrong), there are about 15–20 Labour seats where the margin of victory—not the candidates’ vote share, their margin—is over 50pp.
By contrast, there are barely any Tory seats where the candidate can get 50% of the vote, never mind a margin of 50pp. I believe that the safest Tory seat in the country is Christchurch (near Bournemouth),2 where Christopher Chope won in 2019 with a margin of less than 25,000 votes, or about 47pp. The safest Tory seat in the country, left in the dust by Diane Abbott.
These handful of examples are (of course) not enough in themselves to prove any particular point, although I’m sure any social scientists reading this could construct all sorts of nice statistical measures that would be able to do just that. But I use them just to raise the salience of an idea that (I think) most people would agree to once it’s pointed out: Labour support is much more clustered than Tory support. Labour voters are geographically concentrated in the country’s urban centres, while Tory voters are spread out all over the place. Labour-held constituencies are thus typically much geographically smaller than Tory-held ones (you can see this just by looking at an electoral map!), and are won by larger margins.
But of course, as we are all aware, there is no benefit for Diane Abbott in having such strong support compared to Christopher Chope, or even compared with James Daly (the Tory MP who won his seat by just over 100 votes in 2019). And there’s no benefit for the Labour Party as a whole for having such electorally-successful MPs. Diane Abbott’s margin of 33,000 and James Daly’s margin of 100 translate into exactly the same outcome: one seat each.
I just want to emphasise this. Under our current electoral system, there is no difference between winning with Diane Abbott numbers and winning with James Daly numbers. Once you’ve got even one more vote than your opponents, you are ‘past the post’ as it were; you have won the seat, and it doesn’t matter how many more votes you get. In Diane Abbott’s seat, half of the voters in her constituency—again, not half of her supporters, half of all voters—could have just stayed home in 2019 for all the impact they had on the election. Their votes were essentially wasted.
Many reform proposals fail under these conditions
Vote-wasting has, of course, been discussed for a very long time. Many of the most popular proposals, such as the STV preferred by the Electoral Reform Society and the Lib Dems, are promoted based on their ability to reduce the number of wasted votes. This is a perfectly reasonable idea: vote-wasting is bad, democratic representation is good. But the assumptions that are typically made about how vote-wasting works have become drastically outdated.
In the 1980s, when a lot of modern British electoral reform discourse was fixed (largely by the efforts of the SDP-Liberal Alliance), Labour and the Tories were affected by vote-wasting to a vaguely similar same degree: it didn’t matter a huge amount to either party, and either way it was essentially irrelevant who formed the government. It was the minor parties, especially the SDP and Liberals, who had it bad. But since then, Labour’s industrial heartlands in places like the North of England and South Wales have collapsed (‘Maggie shut down the mines’), leading to high levels of migration to the cities; they have lost their Scottish safe seats; and, crucially, the electorate has become polarised by age to an unprecedented degree, with younger people voting Labour and older people voting Tory in a way not seen before. All of these things have caused the clustering discussed above.
In today’s United Kingdom, the Tories generally get more votes than Labour, but not that many more. The landslide 2019 election should perhaps be treated as an outlier for national purposes, but in 2017 the Tories won 42% of the national vote to Labour’s 40%; in 2015, it was about 37% to 30%. These are by no means insurmountable leads! But, systematically, more Labour votes are wasted than Tory votes. Labour dominance in urban centres, and their high popularity among young people and immigrant groups (both of whom tend to cluster in those same urban centres), means that a larger proportion of their votes are wasted. As such, in 2017, the Tories got about 5% more votes than Labour, but around 20% more seats.3 The Tories also have more safe seats than Labour, seats where they have large and unmoveable leads, precisely because their large leads in these seats are not as large as Labour’s.
In other words, vote-wasting is correlated with party and geography, and it’s getting worse. There are structural forces causing Labour votes to cluster in urban centres, but there are no similar structural forces helping Labour gain more votes to compensate (as the results of the last four general elections show): national Labour gains are generally won on the basis of particular Tory failures or particular popular Labour policies, not secular trends. In a functioning democracy this would be normal and natural; but in the UK it means that over time Labour will be more and more disadvantaged.
Indeed, because this clustering is only getting stronger, it might soon be possible for the Tories to form governments or even win majorities after elections where Labour win more votes. This is not empty speculation: this is exactly what is happening right now in Canada, where right-wing voters are hugely clustered in rural areas (rather than urban areas), allowing the Liberal Party win elections on fewer votes than its main rival. This could soon be Labour’s future; we need electoral reform to remedy this.
Traditional reform procedures, however, are only concerned with reducing the magnitude of vote-wasting, not its distribution. This may have made sense in the past, where vote-wasting was a problem throughout basically all the country, and the worst-affected seats were dotted randomly throughout Great Britain. And it certainly made sense when those proposing electoral reform were smaller parties like the Liberals, with support spread throughout the nation. But in our current situation, reducing the number of wasted votes equally throughout the nation will not overcome the structural advantage of the Tories, or remedy the fact that more votes are wasted in the cities than in the countryside.
To take one example, AV (the reform proposal voted on in 2011) would not stop people like Diane Abbott winning by absurd margins, and thus would not change the fact that most of her supporters waste their votes. Letting people give preferences to candidates beyond their favourite doesn’t help when the problem is too many people in the same seat having the same favourite. The same clustering effects would apply, with the only difference being that we’d have to talk about Labour first preferences being geographically clustered rather than Labour votes. Likewise, the existing Lib Dem proposal of STV is not designed to solve this problem, and (depending on implementation) it seems plausible that it would not.
The general point is that vote-wasting is correlated (by geography and party) today, which is a relatively new phenomenon. But because most discourse about electoral reform is stuck in the 1980s, it tends to just look at reducing the overall number of wasted votes. But such a reform would ultimately just ensure that the structural Tory advantage remained in place.
People should be thinking about this
To be sure, this argument does not apply to all alternative electoral systems. For example, the AMS system used in Scottish and Welsh elections could very plausibly escape this problem and level the playing field between Labour and the Tories (although it would depend on implementation). But in general, it seems that policymakers aren’t really thinking about this, and certainly aren’t designing proposals with geographically-concentrated voter bases in mind. Electoral reform just doesn’t seem to be a policy priority for most people, and those who do care about it are still thinking in the terms set by smaller parties in the 1980s.
I think this is a deep mistake. For one thing, this is a crucial problem for the Labour party, and Labour supporters should care much more about it. If you want Labour to do well, then the fact that both our current voting system and various mainstream alternatives systematically disadvantage Labour should convince you to think harder about electoral reform. Many Labour figures (especially those who can remember the 1980s) associate electoral reform with the ‘Liberals’ and the ‘splitters’, and argue that FPTP strengthens the Labour coalition. This was probably true in the 1980s, but it is true no longer: it is Labour, not the Lib Dems, who are most disadvantaged by our current electoral system, and it is only getting worse for them. If you are Labour-adjacent and care at all about policy, then, you should probably think much more about possible proposals for overcoming your party’s deep structural disadvantage.
Now, those of you who know me will know that I am, um, not the Labour Party’s biggest fan. As such, I am not particularly concerned about the fortunes of the Labour Party in and of itself. But I do care about electoral reform, both for principled reasons (our current system is deeply undemocratic)4 and practical ones (I am a Lib Dem, and almost any imaginable system of electoral reform would be very good for my party). And I think that, if Labour becomes incentivised to care about electoral reform, it could be the best chance the UK has of getting a better electoral system.
In the 1980s, neither Labour nor the Tories had any reason to care about electoral reform: the SDP-Liberal Alliance was thus forced to try and rile up moral indignation with FPTP, a tactic that got John Cleese on board but basically nobody else. But the situation is different today. Labour is facing a deep problem: without Scottish seats, it requires an immense swing for a majority (precisely because of its vote-wasting problem, discussed above), and so if it is to form a government it will likely require co-operation from the SNP or the Lib Dems. The former option has been ruled out, very explicitly, by Keir Starmer; and it seems clear now that the Lib Dems will hold out unless Labour agree to electoral reform.
So electoral reform is a real possibility; but the Labour Party have rejected it recently, precisely because it’s not clear how it benefits them. The Lib Dems are still stuck proposing systems that are obviously designed to benefit them first and foremost. Liberal Democrats have been arguing that the main benefit of STV is that it helps small parties for longer than the Liberal Democrat Party has existed! It’s not immediately obvious how any of these standard proposals would tackle the problems Labour faces: to Labour, it might well seem like a purely self-interested bargaining demand from the Lib Dems. Keir Starmer currently seems quite set against electoral reform proposals, and I have no doubt that is because he sees them as free lunches for the Lib Dems.
But there is no reason why someone could not design a proposal that is a win-win, helping both the Labour Party’s problem of geographically-clustered vote-wasting and the Lib Dems’ struggles with the spoiler effect. Labour will be much more inclined to listen to a Lib Dem coalition agreement if it reads like this: “We will support your government ONLY IF you accept this policy that is good for you anyway.” The problem is coming up with an electoral reform proposal that is obviously and intentionally pro-Labour, rather than vaguely pro-democracy or explicitly pro-Liberal.
If you are a policy researcher today, and you have an idea for an electoral reform proposal that would be obviously good for the Labour Party—that would clearly and intentionally tackle the problem of geographic clustering in vote-wasting—then I think you have a real possibility to make change. Even if you are not a Labour supporter, influencing the proposal that the Lib Dems take to Keir Starmer in any future negotiations could be hugely important: if your ideas or actions make that proposal more palatable to Starmer and his team, it could change the field of play in incredibly valuable ways. Targeting the problem of geographically-concentrated vote-wasting is crucial for moral, democratic reasons; but it is also our best chance to get any electoral reform passed.
If you enjoyed this piece, I’d love to hear from you. I have very little social-scientific or policy expertise, and don’t really know how create more specific recommendations or ideas: any thoughts you might have about anything I’ve written would be much appreciated. I’m on twitter @ptr_mcl, and my email address is petermclemail@gmail.com.
You may have heard recently of a paper by Erik Maskin that does actually suggest that one particular system - the ‘Borda count’ - is in general superior to all others; a good discussion is here. Maskin proceeds by weakening Arrow’s ‘IIA’ condition, and showing that this weakened condition allows for one, rather than zero, ideal voting systems. But, conditional on assuming that we cannot achieve IIA, Maskin’s weakened ‘MIIA’ does not seem to me to be valid except in a handful of particular political situations. (The stylised examples Maskin gives in his paper are instances of these particular situations.) So the Borda count is the best system only in contexts where MIIA is valid, which does not challenge the idea that the best voting system is context-dependent.
I couldn’t actually find great data on this, and wasn’t particularly keen on literally just going through the list of every single Tory seat in the country and ordering them by margin, so this might not be true; if there is a safer Tory seat, please let me know! But the point remains that Labour win their safe seats by much higher margins than the Tories do.
In fact, the same point applies to the 2019 ‘outlier’—the Tories won about 35% more votes, but 80% more seats—but the overall Tory advantage in that election makes the absolute difference less striking.
To be sure, I’m not so unsophisticated to imagine that any mismatch between Commons seats and national votes is undemocratic, and I don’t think we should be aiming to approximate a presidential popular vote. (After all, Arrow tells us that this system too is imperfect, and I think it’s uniquely ill-suited to the UK.) But I do not think that there is any possible justification for systematically disadvantaging a major political party due to the geographical spread of its supporters; and when that disadvantage influences the outcomes of crucial national elections, as it did in 2017, all principled democrats should call for reform.