US Presidential Elections Through the Eyes of a Mathematician. How Much Can You Trust the Polls?

It's been quite a while since the last post on the US presidential election. In the first post on the US election, The US Electoral System Through the Eyes of a Mathematician, we discussed the basics of the US electoral system, in particular the Electoral College, and to better understand what's going on, it's best to first take a look at that post.

A couple of months ago, the situation with forecasts became completely “sour”, it was clear that the current President Joseph Biden chances of re-election are minimal. Some free-thinking analysts even suggested that the only chance for the Democrats was for Donald Trump to drop out of the race for some reason. The reasons could, of course, be different, even the most unconstitutional. Thank God that the assassination attempt failed and Trump is in good health.

As soon as there were suggestions that the Pennsylvania incident was just will add Trump's popularity, as the news feed was broken by the news of Biden ending his election campaign and nominating the current vice president as a new candidate for the presidential post Kamala HarrisThis is where the situation got heated.

Kamala Harris's ratings have now significantly surpassed Joseph Biden's, and current polls suggest new possible outcomes.

A quick look at current polling results in swing states

Let's look at the situation for now with the usual standard view, without delving into some new trends, which we will discuss below. According to the traditional approach to predicting the outcome of the presidential election, the final choice of the winner depends on the results of the vote in the “swing states” (swing states) – states in which voter preferences are unstable and change from election to election.
There are nine states on this list – Arizona, Florida, Georgia, Michigan, Minnesota, Nevada, North Carolina, Pennsylvania and Wisconsin. According to the general opinion of analysts, Florida can now be attributed to Trump's assets, and Minnesota to Harris.
Excluding the remaining seven statesthe Democratic candidate will have the following assets 226 electoral votes, and from the Republicans – 219 votes. Let us recall that in order to win the elections, a candidate must gain 270 electoral votes out of 538 possible.
How might the remaining 93 electoral votes be distributed?

Let's look at the average results of polls published as of August 1.

The diagram shows that if Kamala Harris wins three states – Michigan, Pennsylvania and Wisconsin – she will gain 44 electoral votes and end up with 270 electoral votes, thereby winning by a narrow margin. It is quite possible that the Democratic Party campaign headquarters will focus on this option and choose the governor of Pennsylvania as Harris's vice president. Josh Shapiro. This move, in theory, should add votes to the Democrats in this state and increase the chances of their candidate winning. There is, however, some more nuanceswhich are beyond the scope of our discussion, and we will remain in the world of numbers.

What can be said about the topic in the title of the publication – to what extent can one trust the results of the surveys?

This question can be answered, for example, by looking at the accuracy of the prediction of results. 2020 presidential electionThe diagram shows the average results of polls the day before the presidential election and the final results of the election itself.

I honestly didn't expect to see such, to put it mildly, strange regularity.

In all swing states, except Georgiathe poll results were significantly biased in favor of the Democratic candidate compared to the final results. There are, of course, some considerations as to the cause of such a systematic error. Apparently, many respondents are simply embarrassed to openly say that they will vote for Donald Trump. The results of some interesting polls support this assumption.

For example, in a recent nationwide survey from Civics 49% of respondents supported Kamala Harris, while 45% supported Trump. At the same time, the same 45% believe that Trump will become president, and only 42% believe that Harris will. There is quite a lot of such data, but we will leave the analysis of the reasons for such interesting paradoxes to political scientists and sociologists.

The only thing we can probably predict is that if this is at least one of the reasons for the systematic error in the survey results, then this year, it seems, this error may become even more.

What interesting things are happening in states other than the swing states?

There is a list of states that Joseph Biden won convincingly in 2020, but this year the polls have been quite strong differ from the results of the 2020 presidential election. Guess which way.

There is a rather interesting trend, namely, support for the Democratic candidate has dropped significantly. If we add to this that the 2020 polls predicted Biden to win New Hampshire by 11%, then it seems that we are in for something interesting.

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