Why Even A General Election Cannot Properly Reflect Society's Real Preferences

Providing two thirds of MPs agree in a vote, we learned today that there will be a General Election in June. General Elections score highly on entertainment value, as do weak opposition parties, but how much do they really tell us about the true power of society's political feelings? The answer is, not as much as you may think.

Arrow’s theorem, which I blogged about recently, shows a fundamental fly in the voting ointment – that is, while we as individuals can have properly ordered preferences, society cannot so easily, because society as a whole has no real coherence when those preferences are aggregated. If I'm in the CD store, I'd prefer The Smashing Pumpkins to Sonic Youth, and Sonic Youth to Pearl Jam, which means, quite naturally, I prefer The Smashing Pumpkins to Pearl Jam. Now if Radiohead were introduced into the mix, I'd prefer Radiohead as first choice, which would change my CD preference. In other words, I'd prefer The Smashing Pumpkins CD to the Sonic Youth CD, but by introducing Radiohead, I'll probably end up with the Radiohead CD.

But here's where it gets strange. Introducing Radiohead may naturally mean I now prefer Radiohead to The Smashing Pumpkins, but it shouldn't change the fact that I prefer The Smashing Pumpkins to Sonic Youth, or Sonic Youth to Pearl Jam. But in society things change, because the aggregation of individual preferences into social preferences brings about strange results, whereby, if we stick with the CD store analogy, society may prefer The Smashing Pumpkins to Sonic Youth, but may prefer Sonic Youth to The Smashing Pumpkins if Radiohead are introduced. If society prefers The Smashing Pumpkins to Sonic Youth, then whether Radiohead are an option shouldn't change that fundamental preference - but it does.

So, in politics, you have all these strange things going on, where society might prefer the Labour to the Lib Dems, but with the introduction of the Greens they prefer the Lib Dems to Labour. Or where society might prefer Bernie Sanders to Donald Trump, but with Hillary Clinton in the mix they prefer Donald Trump to Bernie Sanders.

Perhaps the main reason that society as a whole has no real coherence when those preferences are aggregated is that our revealed choices do not zoom in very closely on the strength of feeling behind those choices. A vote for UKIP (like a vote for Brexit) doesn’t capture whether the voter is a xenophobic knucklehead who wants England to be like the 1950s again, or whether the voter is an intelligent and tolerant astrophysicist who simply want less bureaucracy and more free trade. A vote for the Green candidate doesn’t capture whether it’s a conscientious attempt to help save the woodlands, or whether it’s a protest vote against Labour and the Lib Dems - that sort of thing.

Societal preferences in the form of votes do not convey the strength of feeling; they only convey general preferences where if one candidate is successful another one isn't. They don't convey the fact that a quarter of the Green voters are swinging voters or half of the Conservative voters are dyed in the wool, or that there are more people that hate UKIP in the Labour voting camp than there are people that hate Labour in the UKIP camp. These are the strengths of feeling in society that are never properly captured, and as such, the party political demographic that occupies Westminster is merely a shadow of society's political and economic views and feelings.