I haven't looked at your math, but I actually agree, in the sense that I also got about 1 in 1 million when doing the estimate again a week before the election!

I think my 1 in 3 million estimate was about right at the time that I made it. The information that we gained between then and 1 week before the election was that the election remained close, and that Pennsylvania remained the top candidate for the tipping point state.

Could you say more about "practically possible"? What steps do you think one could have taken to have reached, say, a 70% credence?

Oh cool, Scott Alexander just said almost exactly what I wanted to say about your #2 in his latest blog post: https://www.astralcodexten.com/p/congrats-to-polymarket-but-i-still

I don't have time to write a detailed response now (might later), but wanted to flag that I either disagree or "agree denotatively but object connotatively" with most of these. I disagree most strongly with #3: the polls were quite good this year. National and swing state polling averages were only wrong by 1% in terms of Trump's vote share, or in other words 2% in terms of margin of victory. This means that polls provided a really large amount of information.

(I do think that Selzer's polls in particular are overrated, and I will try to articulate that case more carefully if I get around to a longer response.)

Looks like it'll be about 250,000 votes.

I just want to register that, because the election continues to look extremely close, I now think the probability that the election is decided by fewer than 100,000 votes is more like 60%.

I wanted to highlight one particular U.S. House race that Matt Yglesias mentions:

Amish Shah (AZ-01): A former state legislator, Amish Shah won a crowded primary in July. He faces Rep. David Schweikert, a Republican who supported Trump's effort to overturn the 2020 presidential election. Primaries are costly, and in Shah’s pre-primary filing, he reported just $216,508.02 cash on hand compared to $1,548,760.87 for Schweikert.

In addition to running in a swing district, Amish Shah is an advocate for animal rights. See my quick take about him here.

Yeah, it was intended to be a crude order-of-magnitude estimate. See my response to essentially the same objection here.

Thanks for those thoughts! Upvoted and also disagree-voted. Here's a slightly more thorough sketch of my thought in the "How close should we expect 2024 to be" section (which is the one we're disagreeing on):

• I suggest a normal distribution with mean 0 and standard deviation 4-5% as a model of election margins in the tipping-point state. If we take 4% as the standard deviation, then the probability of any given election being within 1% is 20%, and the probability of at least 3/6 elections being within 1% is about 10%, which is pretty high (in my mind, not nearly low enough to reject the hypothesis that this normal distribution model is basically right). If we take 5% as the standard deviation, then that probability drops from 10% to 5.6%.
• I think that any argument that actually elections are eerily close needs to do one of the following:
  • Say that there was something special about 2008 and 2012 that made them fall outside of the reference class of close elections. I.e. there's some special ingredient that can make elections eerily close and it wasn't present in 2008-2012.
    • I'm skeptical of this because it introduces too many epicycles.
  • Say that actually elections are eerily close (maybe standard deviation 2-3% rather than 4-5%) and 2008-2012 were big, unlikely outliers.
    • I'm skeptical of this because 2008 would be a quite unlikely outlier (and 2012 would also be reasonably unlikely).
  • Say that the nature of U.S. politics changed in 2016 and elections are now close, whereas before they weren't.
    • I think this is the most plausible of the three. However, note that the close margins in 2000 and 2004 are not evidence in favor of this hypothesis. I'm tempted to reject this hypothesis on the basis of only having two datapoints in its favor.

(Also, just a side note, but the fact that 2000 was 99.99th percentile is definitely just a coincidence. There's no plausible mechanism pushing it to be that close as opposed to, say, 95th percentile. I actually think the most plausible mechanism is that we're living in a simulation!)

Yeah I agree; I think my analysis there is very crude. The purpose was to establish an order-of-magnitude estimate based on a really simple model.

I think readers should feel free to ignore that part of the post. As I say in the last paragraph:

So my advice: if you're deciding whether to donate to efforts to get Harris elected, plug in my "1 in 3 million" estimate into your own calculation -- the one where you also plug in your beliefs about what's good for the world -- and see where the math takes you.