When people talk about elections like horse racing, the policy doesn’t matter – all we care about is who is likely to win. In this stinking theory of elections, governments tend to represent some sort of unsatisfactory average of voter opinion. Everyone gets a little bit of the things they want, and everyone gets a big dose of the things they don’t want.
Given this model, is it possible that voter opinion is essentially disconnected from election results? Something like that could be the case, according to an all-too-general model of — you guessed it — physicists.
Elections are unfriendly things to model. Put yourself in the position of the party apparatus. In an ideal world, you would come up with policies that you think would improve the nation and then present them to the electorate. That’s a losing strategy. Instead, policies and candidates are selected based on the opinion of voters, who don’t always know what will improve the nation. This creates a close-knit dynamic: the candidates presented are based on the opinion of the electorate and these in turn influence the opinion of the electorate.
This latest research suggests that election models, even without the complication of getting cluttered with reality, can produce alarming dynamics.
The spherical cow election
Imagine if everyone could sum up their political opinion in a single number. Now, in a rational world, everyone would vote for the candidate whose opinion is closest to theirs, meaning their opinion is closest to theirs. In this case, the election results are stable. That does not mean that every election result is the same, but that the public chooses a group of politicians that more or less aligns with the opinion of the majority of voters.
This is a stable electoral system, where a change of opinion in the electorate will be reflected by a change in election results that is about the same size (or maybe a little smaller).
However, we are not rational. Sometimes the closest candidate is still too far from your own opinion. In this case, you may not bother voting. Not voting because of the lack of close representation, it turns out, has deeper consequences than thought.
The researchers define something called negative representation. In the case of negative representation, the opinion of the electorate – or part of the electorate – can shift in one direction, but the election results in the opposite direction. This is what can happen when voters refuse to vote.
Worse, the presence of negative representation can lead to instability. That is, the change in an election result is greater than the change in the opinions of the electorate. Plus, it doesn’t matter if the non-voters are at one end of the spectrum or evenly distributed – the effect is the same.
Show me the wild elections
We know this has elements in most electoral systems, where a significant proportion of voters abstain from voting because they feel no candidate represents them well enough. But wild electoral swings are not observed in those countries. So what’s wrong with the model?
The missing ingredients are electorate polarization and low turnout. When these are added to the mix, small shifts in opinion among the electorate can result in major electoral swings. This behavior in the dynamic model is a “phase transition” and one of them is bad news. When a system undergoes a phase transition, it is very difficult to return to the previous state. That means that if an electorate has ended up in an unstable regime, it is likely to stay there for a long time.
And yes, you guessed it, the researchers point to the United States as a possible example. They examined electorate polarization and claim that it exhibits all the characteristics necessary for instability. Here they even turned the model upside down. The model predicts that with instability the degree of polarization will characteristically increase. The real world data supports that claim.
In short, whatever your political opinion, prepare to be overburdened and depressed by the election results for the foreseeable future.
Physics of Nature, 2020, DOI: 10.1038/s41567-019-0739-6 (About DOIs)