EA - The value of a vote in the 2024 presidential election by Eric Neyman

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: The value of a vote in the 2024 presidential election, published by Eric Neyman on September 1, 2024 on The Effective Altruism Forum.
Summary: A blog post circulating among EAs points out that recent presidential elections have been decided by fewer than 100,000 votes. It may be tempting to conclude that each extra vote in a swing state has a 1-in-100,000 chance of changing the outcome of the 2024 presidential election. In this post, I explain why this is not the case.
I estimate the actual number to be 1-in-3 million for a vote in Pennsylvania (the most important swing state) and 1-in-6 million for a generic "swing state vote". This has important implications for people who are deciding whether to donate to efforts to change the outcome of the 2024 presidential election.
Introduction
Like most readers of this forum, I want Kamala Harris to win the 2024 U.S. presidential election. I also think that electoral politics as a cause area is underrated by EAs, and in 2020 I wrote a blog post arguing that voting for Joe Biden is an effective use of time. To summarize the argument in a paragraph:
If you live in a swing state, there's about a 1 in 10 million chance that your vote will flip the outcome of the entire presidential election. The outcome of the election will influence trillions of dollars in spending. So your vote influences how hundreds of thousands of dollars get spent, in expectation (in addition to non-budgetary considerations).
By the same token, if you support Kamala Harris then you might consider donating to efforts to get her elected. If you can get her one extra swing-state vote for $1,000 (that's my best guess), that means that you can spend $1,000 to influence how hundreds of thousands of dollars get spent.
Is that a good deal, compared with other EA interventions? Maybe! I usually estimate that the U.S. government saves about one life per $10 million that it spends well. If you believe this guess, you'd be saving a life for about $10k-100k, which is... fine but worse than interventions like the Against Malaria Foundation. (Of course, it's much more complicated than that.[1])
But what if you thought that one extra swing-state vote increased Harris' chances of winning by 1 in 100 thousand? In that case, you'd be spending $1,000 to influence how tens of millions of dollars get spent. That's a really good deal -- literally a 100x better deal -- and is probably worth it!
Where does the number 100 thousand come from? The anonymous blog "Make Trump Lose Again" (MTLA) makes the case that some interventions to help Harris get elected are really cost-effective. Quoting from the blog post:
Biden won the last election by 42,918 combined votes in three swing states. Trump won the election before that by 77,744 votes. In 2000, just 537 votes (and likely some Republican meddling) in Florida decided the election for Bush, who won a second term by 118,601 votes in 2004.
There's a good chance the 2024 election will be extremely close too. [Emphasis original.]
(What does it mean that Biden won by 42,918 votes? If Trump had won Arizona, Georgia, and Wisconsin, he would have won the election. He would have needed 10,457 more votes in Arizona, 11,779 more votes in Georgia, and 20,682 more votes in Wisconsin, for a total of 42,918 votes.)
It may be tempting to draw the conclusion that an extra swing-state vote will increase Harris' chances of winning by 1 in 100 thousand. Indeed, a couple of people I've talked to implicitly had that takeaway from the blog post. But as I will argue, such a conclusion is unwarranted.
This post has two parts. In Part 1, I explain why the quote from MTLA does not straightforwardly translate to an estimate of the impact of a marginal vote. Specifically, I argue that:
(The less important reason) It is a coincidence that three of the last six elect...