I'll have a number of posts on this election--this one will consider a number of things that I found interesting but don't need a full post.
1. Many people are talking about the terrible failure of the polls, often reviving the idea of "shy Trump voters." It does sound like there were some substantial mistakes in some state polls, but the national polls weren't far off. The final Economist forecast based on an average of polls gave Biden 54.4% of the two-party vote. If 2% voted for third parties, that would mean 53.3% Biden and 44.7 Trump. Not all of the votes have been counted yet, but I estimate that the final will be 50.9% Biden and 47.1% Trump. So the polls were off by about 2.5%. That's not unusual--there are often errors of about that size. They don't have any clear pattern--sometimes they favor the Democrat, sometimes the Republican, sometimes the incumbent, sometimes the challenger. There's a Wikipedia page on the history of presidential election polling that gives figures from the Gallup poll. For example, in 1996, the average of the last 10 polls (October and November) was 51.4% for Clinton and 36.3% for Dole. The election returns were 49.2% for Clinton and 40.7% for Dole. In 2000, almost all polls showed Bush ahead, usually by about 4-5 points. Of course, Gore was slightly ahead in the actual results.
So although the polls were off, they weren't off by an unusually large amount. But in a close election, any difference becomes more noticeable. People talked about the 1996 error at the time, but have forgotten it because Clinton won easily anyway.
2. That leads to my second point--that recent presidential elections have all been close. I knew this alread, but when I looked at the data I was surprised at how large the change had been. If you define a landslide as a win by a margin of 10% or more, 11 of the 25 elections from 1900 to 1996 were landslides. There have been no landslides in the 21st century, in fact none since 1984, so we have set a record for the longest gap between landslide elections (the previous record was 1872-1904). A plot of the absolute value of the margin over time in elections from 1864-2016:
My original purpose in compiling these data was to look at the relationship between popular vote and electoral vote. Here it is, with the Republican share of the two party vote (centered at zero, so 60% Republican is 0.1, 45% Republican is -.05, etc) on the horizontal axis and the log of the ratio of Republican to Democratic electoral votes on the vertical.
That's close to a linear relationship, except for some outliers at the high end of Republican vote. They occurred in the days of the "solid South," when the Southern states voted Democratic regardless of what the rest of the country did, which put a ceiling on the potential Republican majority in the electoral college I excluded the four elections where the Republican share of the two party vote was over 60% (it would have made more sense to leave 1972 in, but that rule excluded it), and estimated a regression, then calculated the probability of winning the electoral college at various shares of the popular vote, assuming the errors have a normal distribution.
popular vote share Chance of winning EC
50% 50%
50.5% 69%
51% 84%
51.5% 97.5%
52% 99%
I didn't report this before because it was more of an amusement than a serious analysis, but given recent history, the question of how big a lead in the popular vote has to be before you can be pretty sure of winning the electoral college is important. I assumed a constant error variance, which probably isn't right--it seems to increase as the election gets more lopsided. Adjusting for that would increase the chance that the winner of the popular vote would lose the Electoral College.
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