A sideways look at economics

A survey by Pew Research Centre last October, just one month before US voters headed to the polls, found that 89% of President Trump’s supporters and 90% of Joe Biden’s thought the election of the other candidate “would lead to lasting harm to the US”. In the end the result was fairly close, especially in terms of the electoral college ‒ as it usually is in US presidential elections. But that closeness does not mean that the preferences of the voters were close: quite the opposite. The voters appear to have been highly polarised, more so than for the last few decades at least. How have we got here, and what does it mean for democracy?

A two-party system is supposed to deliver a battle for the median voter, according to the late US statistician Harold Hotelling (see previous Fathom research). But the US is proving Hotelling wrong. The Trump campaign was battling to secure the votes of a highly motivated base that was not close to the median voter in terms of their political preferences. OK, they lost – but last time around they won, with the same approach. That change of approach, the move away from the median voter, is driven by something.

Is it the voting system? The US electoral college is a curious relic of the formation of the Union, which results in a huge overweight on the votes cast in certain states and underweight on votes cast in others. Starting from a blank sheet of paper, you would not design a system like that. But in the US, as everywhere else (perhaps, above all, in the UK) the sheet of paper is never blank. In the US, there is a constitution written on it.

To explore this issue, let’s imagine a simple example of linear preferences… how to correctly serve scones. Voters’ preferences range from die-hard supporters of the Cornish method (jam first then cream) or the Devonshire method (cream then jam… urgh). As the chart below reflects, when there are two candidates, a simple ‘one-person-one-vote’ system, called Plurality, is effective. Candidate 1’s alignment allows them to take the majority of votes and as a result they win the election. The same applies, incidentally, to the debate about scones. While you may wish to suggest that the question of how one eats one’s scones should be a matter for personal choice, not the dictate of the majority, this author disagrees ‒ on the presumption, surely correct, that the majority is with him.

But the introduction of a third candidate, one who not only likes jam first then cream but also chocolate chips on top, makes matters much more complicated, and introduces sometimes serious anomalies (and also concerns for their mental health).

When the anomalies are substantial, changes in the voting system should be considered. No system is perfect, but that does not mean the US voting system could not be improved: in my own life, perfect physical fitness is as distant as the stars, but that doesn’t mean I shouldn’t bother going for a run occasionally or try eating fewer carbs. Some anomalies in the US electoral system that could and maybe should be addressed were illustrated by the so-called ‘Nader effect’ that was in play in the election that brought George W Bush to power in 2000. The election came down to the state of Florida. Ultimately, Bush won the state (and consequently the presidency) by just 537 votes. The reason was down to Ralph Nader. While not a serious contender for the presidency, he gained the support of almost 100 thousand voters in Florida, the majority of whom were established, later, to strongly prefer a Gore presidency over a Bush one. If Nader hadn’t run, Gore would likely have been president.

The diagram below shows the Nader effect in play. Those lunatics who want to add chocolate chips to their scones are shown next to the jam-firsts, on the assumption that more of those lunatics belong to the otherwise sensible, jam-first majority than to the cream-first fringe — thus splitting the jam-first group and allowing the cream-first crazies to take over.

As a result of these and other apparent anomalies, some are arguing that it would be better to shift to an Instant Runoff system in the US, referred to as Single Transferable Vote in the UK. Instant Runoff elections begin with voters ranking all candidates. In each runoff the candidate with the least number of first choice votes is eliminated, and the result is recalculated using the second choice of the eliminated candidate’s voters. In Instant Runoff elections, voters aren’t incentivised to choose solely between the top two candidates. This system nicely avoids the Nader effect by allowing split votes between two similar candidates to be resolved in an automatic runoff.

Now before you start making your placards in support of Instant Runoff, there are flaws in this system as well. The “Centre Squeeze” phenomenon is the process whereby centrist candidates with broad support fail to survive runoffs with other opposing candidates who are closer to the political poles. Using the same example with three candidates, but altering their position, you can see that Candidate 1, calling for jam and cream but allowing individuals to make their own choice about the order in which those are applied, will fail to pass the first runoff due to having the fewest first choice voters. This is despite a majority of voters preferring Candidate 1 to Candidate 2, and also Candidate 1 to Candidate 3. A second runoff in this example would see Candidate 2, the cream-first crazies, narrowly winning, due to them being preferred over Candidate 3 by a majority of voters. There is an incentive here for Candidate 3 voters, the chocolate chip odd-balls, to tactically betray their favourite to ensure a victory for Candidate 1 (any which way) so at least they are allowed to persist with their preferred (but curious) ordering. So, whilst Instant Runoff can avoid some of the issues Plurality falls victim to, there are still outcomes in which this system can elect a leader at odds with the preference of most voters.

Let’s look at another alternative, Approval voting. Like Plurality, it is also a straightforward system, but instead of ‘one person, one vote’, voters can vote for as many, or as few, candidates as they’d like. That means a voter whose preference is between Candidate 1 and 2 no longer has to choose between them but can instead vote for both. In this system, if voters act honestly, there is no spoiler effect from an extra candidate, as in Plurality and Instant Runoff. The only way a new candidate can alter the result is if they win. The same situation which resulted in the “Centre Squeeze” phenomenon under Instant Runoff, instead results in Candidate 1 being declared the winner when using Approval voting.^[1]

Sounds great, but surprise surprise… voters don’t always act honestly and, as with the other systems outlined, Approval voting also has room for voters to be strategic. In order to boost the chances of their favoured candidate, Candidate 2 voters who also approve of Candidate 1 can tactically not vote for 1 and vice-versa, resulting in a situation aptly named the “Chicken dilemma”. Each group of voters engage in a game of chicken with the other, taking votes away from their less-preferred candidate and potentially leading to the election of Candidate 3 – the choc-chip chumps – which neither group prefers. That would be a bit like actually electing Ralph Nader.

While these alternatives do produce results which are as good as or better than Plurality, and less anomalous for a wider range of voting outcomes, including all outcomes for which Plurality performs optimally, they still have flaws. As a previous TFIF has explained, Arrow’s Impossibility Theorem goes further by proving that no voting system can clearly translate individual preferences into a social ordering. Still, in theory, Instant Runoff and Approval voting, just two examples from many alternatives, are strictly better electoral systems than Plurality (and not just because they result in a Cornish victory).

Ultimately, all voting systems can create anomalies and it’s up to the voters to decide whether they’re ready to compromise on their ideal outcome in order to avoid the worst outcomes from their perspective. Sometimes they will choose to vote tactically, other times they will not. It’s not the voting system that matters: it’s the voters. The voting system does not have to be perfect (and it can’t be) – it just needs to be good enough to secure what is known as ‘loser’s consent’. Those who cast their votes for the losing candidate need to have sufficient trust in the voting system, for all its imperfections, to accept the result and consent to a peaceful handover of power if that is what the election calls for. That is the point of democracy.

It doesn’t really matter who wins, in the grand scheme of things: it matters that the incumbent can be ousted peacefully. It is absolutely vital that that holds, even when the voters are extremely polarised. The recent US election showed that US democracy is stronger even than the extremely powerful forces of polarisation in place in US society (and elsewhere too). Long may it last.

[1] I’m assuming here that voters pick candidates which fall within an arbitrary distance of their own preference and, failing that, the candidate that they are closest to.