Why Polls are Wrong: The Uncertainty Principle for Elections


by David K. Levine, November 2016

Physicists cannot predict the movement of a particle. Economists cannot predict market crashes. Political scientists cannot predict the outcome of elections. The failure of physicists has a name “Heisenberg's uncertainty principle” and to my knowledge nobody criticizes physicists for their failure. Economists and political scientists are much criticized for failing to forecast market crashes and elections. This is odd: the uncertainty principle is the foundation of quantum mechanics in which spooky particles seem to anticipate what other particles will do. The failure of economists and political scientists is for the much less spooky reason that people can and do anticipate what other people will do. There is no name for the failure of economists and political scientists: perhaps it will be more acceptable if we make it a principle? The “Lucas critique?” The “Neumann principle?”

rock-paper-scissors                      To understand why social scientists are necessarily unable to predict certain things let’s start with something simple - the familiar game of rock-paper-scissors. As we know rock breaks scissors, paper wraps the rock and scissors cuts the paper. Suppose Jan and Dean are playing rock-paper-scissors and Nate interviews each of them. Jan tells Nate she is going to play rock and Dean tells Nate he is going to play scissors. Nate publishes his prediction on his website: Jan is going to beat Dean by playing rock to his scissors. They play the game: Jan plays rock and Dean - no fool he - plays paper and beats Jan. Oops...looks like Nate was wrong. As John Von Neumann showed in 1928 there is only one solution to this paradox: Jan and Dean cannot know how the other is going to play - they must be uncertain. That uncertainty can be quantified: each must believe the other has one chance in three of playing rock, paper or scissors - or one of them is either stupid or wrong. Only if Nate announces that there is a 1/3rd chance of Jan and Dean each playing rock, paper or scissors will Jan and Dean be content to play as he forecasts. Empirical research shows that in real contests - soccer matches, tennis matches - the good players play randomly and with the right probabilities.

crash No doubt some investors and voters are stupid and wrong - but most are not. Suppose that clever Nate discovers from his big data analysis that the stock market will crash next week. He announces his discovery to the world. Are you going to wait until next week to sell your stocks? Well nobody else is, so the market is going to crash today. Oops...looks like Nate was wrong again. Just like rock-paper-scissors the only prediction Nate can make that is correct and widely believed is a probabilistic one: For example, he can  tell you that every day there is an .01% chance of a stock market crash - but he can’t tell you when the crash will take place. Just as the uncertainty principle underlies quantum mechanics so the fact that people react to forecasts is the basis of rational expectations theory in economics. And just as in the simple rock, paper scissors example this theory enables us to quantify our uncertainty.

So elections. People vote for lots of reasons - out of civic duty, to register their opinion - and to help their side win. In 2012 voter turnout in swing states was 7.4% higher than in other states. Any analysis of elections must take into account that there are marginal voters behave strategically - who only vote if they think there is a chance they might contribute to victory. If you are certain your party is going to lose are you more or less inclined to vote? If you are certain it is going to win? Many people - like those in the states that are not swing states - are less inclined to vote when they are confident of the outcome. So when Nate comes along and tells us that the Democrats are definitely going to win, what does the marginal Republican voter Dean do? Skips the vote. But Jan is no dummy, she realizes since Dean isn’t going to vote, she needn't bother either: her Democrats can win without her. But...Dean should anticipate Jan and and vote and so bring his own party to victory. Again: there is no solution to this problem that does not involve uncertainty about the outcome.

Why are polls wrong? Because people lie to pollsters? Because people change their minds at the last minute? By and large this isn’t the case - even in upset victories polls do a pretty good job of predicting how people are going to vote. What they do not do is do a good job of predicting who is going to vote - they do not predict turnout well. You read this all the time “this year turnout among Hispanic voters was unusually low” and so forth. You get the idea? We may know how many Democrats and Republicans there are and we may know that they are all going to vote for their own candidate: but if we don’t know who is going to turn up at the polls we don’t know who is going to win the election. And whether voters expect their party to win or lose changes whether they will bother to vote - so that voter turnout is subject to the Neumann uncertainty principle.

Pollsters argue about their mistakes. Some understand that they do not do a good job of predicting turnout. Some - Sam Wang and his Princeton Election Consortium - made the ludicrous claim - based on”deep math” - that there was a 99% probability that Hillary Clinton would win the election. Nate Silver was more conservative giving her only a 73% chance of winning. But as far as I can tell, neither one realizes that there isn’t something wrong with their models - that the reason that they do not predict the election is because they cannot predict the election.

Political economists do understand this, at least in principle, and indeed can quantify it. There are a variety of models capturing the strategic element of electoral turnout - my favorite is my own paper with Andrea Mattozzi “Voter Participation with Collusive Parties” - but all of these papers have one thing in common: the outcome of the election must be uncertain. We do not put sufficient emphasis on this and have done a poor job of communicating with the rest of the world - but any forecasts of elections that do not take account of the Neumann uncertainty principle are bound to fail.