Choose your own 538 adventure

Like lots of others, I’m anxiously watching forecasts of the US election outcome. But it’s hard to figure out what’s going on, with Biden way ahead in the polls, behind in the betting markets and rated a 70 per cent chance by the model at 538.com. Inspired by this post from Andrew Gelman, who is working on the Economist model (Biden currently a bit over 80 per cent), and an informative tweet from Nate Silver, I’ve managed to improve my own understanding a bit. At least I think so.

Silver’s tweet confirms that the Electoral College system gives Trump a significant advantage relative to an election by popular vote. He syas
Chance of a Biden Electoral college win if he wins the popular vote by X points:

0-1 points: just 6%!
1-2 points: 22%
2-3 points: 46%
3-4 points: 74%
4-5 points: 89%
5-6 points: 98%
6-7 points: 99%

With that information, it’s easy enough to fit a normal distribution to the margin, and get an estimate probability of winning. By fiddling with the numbers, it’s easy to replicate the 538 probability estimate and also to get a probability distribution looking fairly similar to those displayed on te site. My best estimate is N(5,4), that is, the mean value for the margin is 5 points and the standard deviation is 4. The mean value is consistent with the description of the state level estimates on the 538 site, which (very roughly speaking) take the existing polls (which currently have Biden ahead by 7.4 nationally) and then give Trump 1 point for an incumbency advantage (reducing the margin by 2 points).

Looking at the Economist model (which doesn’t necessarily agree with 538 on the exact distribution of the Electoral College advantage) it fits pretty well with N(6,3)

The standard deviation is a big deal here. N(5,4) implies a 95 cent range of, roughly, -3 to 13. I can’t say I find this plausible, at least assuming the election proceeds without armed intervention. Short of personally inventing a vaccine and hand-delivering it to the entire US population, I can’t imagine anything that would give Trump a 2.5 per cent chance of winning the popular vote. And it’s equally hard to see what would push him much lower than he is now.

If you would like a more optimistic story, you can get one by focusing exclusively on the polls where Biden’s lead has been consistently between 7 and 9 points, consistent with a distribution like N(8, 0.5), which puts Biden at 99 per cent.

I should alert readers that I don’t always get this kind of calculation correct, so feel free to check it out and correct it if necessary.

8 thoughts on “Choose your own 538 adventure

  1. If Biden wins the Military Industrial Complex wins. If Trump wiins the Military Industrial Complex wins.
    If the Miltiary Industrial Complex wins the vast majority of the people of planet earth, including the vast majority of people of the United States, the United Kingdom, Canada, Australia and New Zealand lose.
    Once we have bio sphere collapse everyone loses.

    Can anything be done? Some say that the window of opportunity is still open, though just barely.
    I smell poison gas flowing through that crack in the window. Is it a flamable gas?

  2. There’s this old book, probably the first to the popular why is there no socialism in the US theme, written around 1900 maybe? It compares railroad death between the US and European nations. The US death rate was much higher – which the author took to mean that individual life would be valued less there even back then. In the last decades, certain rather dysfunctional aspects of US culture did not exactly improve.

    Mass death don’t seem to have caused any new iconic pictures of desperate hospital staff close to mental breakdown during an interview, falling asleep at a chair, or like the mass graves in New York dominating the news. Meanwhile, Spain’s current numbers are starting to exceed US levels, which is not a good sign. There is someone “worse” to point fingers at now without distorting reality too much. That Spain managed to be so undisciplined so fast after they had a full scale health system breakdown disaster not too long ago, that is no good sign regarding human nature in general within a more reasonable societal context. So with a lack of media transmission and “just” something around one in 1000 or one in 300 dying from COVID-19, not all of them obvious, long term effects among survivors also not quite visible. Wouldn’t put it entirely beyond imagination anymore that a majority of US voters do end up with a Trumpish attitude towards COVID-19. The old mixture of lies, propaganda and the toxic self-centered identity many people have to develop to stay functional within that society still seem to work. Basically a month ago my prognosis was that reality would hit with such a big hammer that Trump had 0 chance. Now I´m not so sure anymore, if the Hammer not quite reaching New York 2.0 dimensions so far might not be enough for Trump to have some chance left.

  3. Like most analysts, Nate Silver was wrong on the POTUS election last time. I really hope he is right this time…

  4. What is the question the polls are trying to answer? If they are a snapshot of current attitudes – and whether they have changed – they have no history and the SD is what they say, or less by aggregation. “Is it raining today?” But if you take them as a record of fixed preferences (“Do you like Marmite / Roquedort cheese?”), then the samples can be added: more than a million over Trump’s incumbency, and the SD is effectively zero. In reality, votes reflect both stable attitudes and changing information.

    The mix changes between elections. Trump and Clinton were both widely disliked, so preferences were volatile. Everything suggests that attitudes to both Trump and Biden are very stable, to Biden’s advantage. In a fair election, Biden will win easily, even with the Electoral College bias. Of course, the election may not be fair. My hope here is that Trump’s incompetence will keep him from successful vote-rigging, and for subordinates the fear of prosecution for electoral fraud if Biden and Harris – especially Harris – win. The more open question is control of the Senate.

  5. hix, you say intersting things, but they are hard to read. Please break up you rparagraphs into one, two, or three sentences. That style is much easier to read on a LCD monitor than long involved paragraphs.

    Thaks!

  6. Do you like Marmite / Roquedort cheese?

    There’s a cheese called Marmite/Roquedort?

    No, probably not. But that’s what happens in my head when you write things like that.

  7. Nate Silver would give Biden a 90% + chance for an election held today. His model assumes a better than even chance that things will move in Trumps favour by the actual day of the election (based on trends in previous elections and perhaps other things).

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