What we know for certain about the US election — and what we don't

Werner Heisenberg would have understood the merits of opinion polls — and their limitations. He was the physicist who proposed the Uncertainty Principle, the idea that the observation of tiny, sub-atomic particles can provide powerful insights but never guarantee precision.

Much the same can be said of opinion polls. Applying Heisenberg’s principle to the current American election campaign, what can we say about the state of the race between Joe Biden and Donald Trump? We can separate those things that are definitely true, those that are probably true, and those that defy certainty.

Definitely true

It is definitely true that support for both candidates has barely changed since early June. There are two ways to demonstrate this (and show why oscillations in the figures from individual companies reflect nothing more than random sampling fluctuations). First, we can do this by logging the results from polling companies that survey voters at least once a week. This gives us a like-with-like picture of how voters’ views have evolved. For the past three months, the three-poll weekly average of the figures reported by YouGov, Ipsos and Morning Consult has been 9 per cent plus or minus one — statistically no change.

That doesn’t mean there has been no movement at all. Biden and Trump may have benefitted from small gains immediately after their parties’ conventions, but these were small and short-lived.

The second way to track the race is to spread our net more widely and gather the data from all the companies conducting national polls, regardless of their frequency. The 538 website provides the most sophisticated daily rolling average. Since early June, 538’s daily figures have stayed within narrow ranges: Biden 50.5 per cent, Trump 42 per cent, in both cases plus or minus one. Such stability for more than three months at this stage of an election campaign is unprecedented.

Probably true

Next, it is probably true that if the election were held this week, Joe Biden would win comfortably. As I argued two weeks ago, he is attracting substantially more support from moderates than Hillary Clinton did four years ago.

However, this is where a polling version of Heisenberg’s Uncertainty Principle kicks in. Individual polls are subject to two sources of error. There can be random sampling fluctuations, which no pollster can avoid. There may also be systematic errors — unknown biases in the way samples are designed and the raw data weighted. The risk of random error is largely removed by combining results from a wide range of polls. This irons out their random differences. It is why we can be confident about the stability of the race in the past three months. But systematic errors cannot be ironed out and they can’t be measured until the election is over.

In 2016, the national polls came close: on average their eve-of-election surveys predicted that Hillary Clinton would win the two-party vote by 52-48 per cent; in the event she led Trump by 51-49 per cent. Indeed, in modern times, eve-of-election polling averages have provided a reasonable guide to the actual share of the vote: within 1.6 points of the two-party share for each candidate at each election, and therefore within 3.2 points of the gap between the two candidates.

Given all that, we can be reasonably sure that Biden’s lead has remained steady over the past three months, but less sure about the size of that steady lead. Polling history suggests that Biden’s recent nine-point polling lead means that he is at least six points ahead in reality — and could be up to 12 points ahead.

Cannot be certain

Finally, we cannot be certain who will win on 3 November. For a start, the election will be decided not by the national vote but the result in a handful of states that Trump won narrowly four years ago. Polls in these states are more relevant than national surveys, but less reliable. There are fewer of them (so it is harder to iron out random fluctuations), they often have smaller samples than national polls, and historically they have been less accurate. The table below tells the story. It shows the polling averages in seven of Biden’s target states, according to the 538 website, a) immediately before election day in 2016, and b) today, and compares these with the state-by-state figures four years ago.

The good news for Biden is that there has been a shift in his direction in every state since 2016, whether the comparison is with the polls last time or the actual result. However, Trump did better than the polls in every state — albeit only marginally in Florida and Texas, and modestly in Arizona. But in the other four states the polls were clearly adrift.

This raises the question: how much has opinion really shifted in these states? If we compare recent polls with the votes cast in 2016, Biden is well up in all seven states, and by 6.8 points on average. On these figures, Biden should not just win, but win big. However, if we compare the latest polls not with the 2016 votes but with what the final polls predicted, the story changes. Biden is still on course for victory, but with little room to spare. A bad TV debate, or a lower turnout among his supporters, or problems with mail-in ballots… It’s not impossible to see Trump once again winning the electoral college while losing the nationwide popular vote.

Which story is more plausible? Most American polls have revised their methods in the battleground states in light of their failures last time. They hope not to repeat their mistakes. But as I know from my experience in running election polls in Britain, the elimination of old mistakes provides no guarantee of avoiding new errors.

As things stand, Trump would need to overcome the biggest polling deficit of any incumbent President since 1948 if he is to keep his job. If Biden wins each of six target states where he currently leads in the polls, he would defeat Trump comfortably, by 333-205 in the electoral college. Victory in all seven, including Texas, would convert that into a 369-169 landslide. However, the Uncertainty Principle lurks round every polling corner. The 538 site’s prediction model currently gives Biden a 75 per cent chance of victory against a far-from-negligible 25 per cent chance for Trump. That looks about right.