Just for entertainment, I wrote a program that simulates the US presidential election of 2020. (I was interested in seeing whether, for example, predictit's relatively low probability of Biden's winning the election could be reconciled with its relatively high probability of his winning Pennsylvania.) The program assumes that between now and election day, voting in each state will change by some amount. This change is modeled as the sum of two normal (Gaussian) random variables, one of which is nationwide and the other per-state. This question is about how big to make the first variable's standard deviation, which I notate as A.

I've found data showing that historically, state polling from a week or two before election day has a mean absolute error of about 5% in predicting the national popular vote, which is quite small. However, it's only July now, and traditionally most voters would not have paid much attention at all to a presidential election this early in an election year. Therefore you would expect the correct value of A to be much higher. That is, there is plenty of time for events to occur and for people to make up their minds or change their minds.

Can anyone point me to any historical data on how big these fluctuations are likely to be when x amount of time remains until election day? (The 2020 election may be different, because Trump is so polarizing and so many people have already made up their minds about him, but that would be a different topic. Right now I'm just looking for historical data.)

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    Have you looked at fivethirtyeight.com? They do extensive modeling of this sort for every election... – jeffronicus Jul 17 '20 at 17:58
  • @jeffronicus: Are you asking whether I've looked at their predictions, or whether I've looked at a description of the mathematical internals of their modeling? If the former, then I don't think they publish predictions of the kind of thing described in the question, such as the conditional probability that Biden loses given that he wins in Pennsylvania. If the latter, then no, and it would be helpful if you could point me to such a description. – Ben Crowell Jul 17 '20 at 18:15
  • @jeffronicus: Your comment prompted me to look up how fivethirtyeight's model works. I found a description here: election.princeton.edu/2012/11/04/… It seems to be a totally different type of model, and therefore not really applicable to what I'm trying to do. – Ben Crowell Jul 17 '20 at 18:33
  • there's a lot of sites with graphs and tables of state-level polling over time. all you need to do is compute the avg deviation x days out. – dandavis Jul 17 '20 at 19:17

I did some more web searching, and I found some information that seems to answer my own question.

This site has polling errors for the popular vote in the last 10 presidential elections. Twelve months out, the average absolute error is about 12%, 4 months out is 9%, and in the final month 2.5%.

If you restrict attention only to more recent elections (1996-2016), then you get a very different picture. The average absolute error is somewhere around 5%, and it doesn't go down much except when you get very close to the election. They don't comment on why this is. It could be that partisanship has gotten stronger, or that pollsters have gotten better at their jobs, or it could just be a coincidence that the the last 6 elections behaved this way. When the error is as small as 5%, you're mainly measuring polling error, not true shifts in voters' opinions.

I'm actually interested in state voting, not the popular vote, so this is not exactly what I needed. However, it seems reasonable to roughly double these numbers for state polling, since, as described in the link in the question, state polling errors in the final month are typically about 5% (smaller for states that have been well polled).

  • how are you calculating %? If an early poll says 48%-42%, and the result is 53%-47%, is that really error? – dandavis Jul 20 '20 at 9:20
  • @dandavis: I think they're working with differences, so in your example the poll said +6 and the result was +6. – Ben Crowell Jul 20 '20 at 20:17

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