DESPITE POLLS being in essence tied, gamblers betting on the outcome of America’s presidential election are increasingly confident that Donald Trump, the Republican nominee, will win. Polymarket, a prediction market that has seen over $2.6bn traded on the election, gives him a two-in-three chance. Bettors are in effect gambling that polls are underestimating him for the third time in a row.

Such an error is certainly possible. Polling averages show Kamala Harris or Mr Trump leading in each of the seven swing states by a smaller margin than a normal polling error (see chart). Democrats fear there will be a repeat of the substantial polling misses of  2016 and 2020, when Mr Trump did better than expected. But there is no guarantee that the error will be in the same direction this year: pollsters have gone to great lengths to account for previous mistakes. As The Economist’s presidential forecast quantifies, based on historical polling errors, a broad range of results are possible on election day—but polls remain the best indication of how people intend to vote.

Opinion polling works by surveying a representative sample of voters. Errors can arise in a number of ways. There is normal statistical variation, which affects all polls, especially those with a small sample size. There is the risk of last-minute swings or unexpected turnout patterns. And there is the biggest headache for pollsters—ensuring their sample is representative. Researchers work hard to do this: finding new ways of reaching voters, incentivising respondents from certain demographic groups and using “weights” to increase the relative importance of underrepresented groups.

FiveThirtyEight, a data-journalism outfit, has calculated polling averages for presidential elections going back to 1976. On average, the size of the gap between the polls’ findings and the actual margin of victory is 2.7 percentage points nationwide and 4.2 points in individual states. FiveThirtyEight currently estimates that the largest lead for either candidate in the seven swing states is just 2.0 points, for Mr Trump in Arizona.

Infamously, polls in 2016 and 2020 systematically underestimated Mr Trump’s vote, especially in battleground states. After the 2016 election, the post mortem conducted by AAPOR, a professional organisation of pollsters, pointed to a late swing towards the Republican nominee and overrepresentation of graduates in poll samples. Most firms began to weight their samples to do a better job of reflecting the education profile of voters.

In 2020 the underestimation of Mr Trump was repeated for different reasons. This time AAPOR identified non-response bias—Republican voters were less likely to respond to pollsters. One theory is that they were less likely to be at home during the covid-19 pandemic (twiddling their thumbs and responding to surveys). Another is that Republican voters distrust pollsters, which discourages them from answering surveys.

Since 2020 pollsters have been at pains to reach a representative sample. They have experimented with recruitment that appeals to certain sections of society (postcards plastered with patriotic imagery, for example) and new modes, such as text messages. It is anyone’s guess whether this will be enough to account for the Democratic bias in response rates or whether supporters of Mr Trump are still reluctant to answer polls. If the errors seen in 2020 or 2016 are repeated even to a small degree that would be disastrous for Ms Harris—she could lose all seven swing states.

Democrats aiming to soothe their anxieties may refer to a wider historical lens. It is true that there is a slight correlation between the polling error in a state at one election and the error in the next. That suggests that Mr Trump is more likely to outperform the polls than Ms Harris is. But the relationship is weak and not very useful for predicting election results. There are also plenty of plausible scenarios in which polls underestimate support for Ms Harris. For example, the errors in 2020 could have been pandemic-specific. Pollsters may have since overcorrected for them. Polls, with all their uncertainties, remain the most useful indicator of public opinion. Without them we would not be able to say with such confidence that the outcome of the election is a toss-up. ■