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Decius comments on Voting is like donating thousands of dollars to charity - Less Wrong
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Nope. Half the votes prevent a Romney victory, and the other half prevent an Obama victory.
Your confusion is understandable, especially since I confused myself and started bullshitting you for a while before rederiving what I did in the first place. Sorry about that.
That's right. Sorry, I shouldn't have been stressing the high correlations between voting fluctuations in different states.
Ah, ok.
Numbers from your toy example: Pr(Blue tied) = 0.1% Pr(Blue decisive | Blue tied) = 90% Pr(Blue decisive) = 0.1% implications: Pr(Blue decisive and tied) = 0.09% Pr(Blue decisive and not tied) = 0.01% This is not plausible. Presumably Pr(Blue decisive and votes blue by 1 vote) is also roughly 0.09%, in which case Pr(Blue decisive and not tied) cannot possibly be less than that. Assuming Red never enters the picture, Blue is decisive whenever it ends up voting more reddish than Purple does. Given how often Blue ties, I would expect this to actually happen fairly frequently.
Apologies for the slow response; I've been unreasonably busy. Executive summary of what follows: Yup, you were right.
So I tried generating more realistic numbers with the general structure of my toy example, and my conclusion is: Oops, you're right and my example is no good. Sorry. And I think I agree with your simple probability-pushing argument that 538's probability for California being decisive isn't consistent with the numbers from Gelman et al being applicable in the 2012 election.
So, it seems to me that there are (at least) the following possibilities. (1) Gelman et al had a good model, and it remains reasonably applicable now, and 538 had too low a probability of California being decisive. (2) Gelman et al had a good model, but the political landscape has changed, and now California is less likely to be decisive than their model said it was in 1992. (3) Gelman et al had a screwed-up model, and their probabilities weren't right even in 1992.
I agree with you that #2 is the least likely of these, and I offer the following statistic which, if cited at the outset, might have saved us a good deal of argument :-). In 1998, California went Democratic by about 51:48. In 2012, California went Democratic by about 59:39.
I accordingly agree with you: Academian's numbers for his own case, which used the Gelman et al figures for California, likely gave much too high an expected value for his vote in California.
I assume you meant #2 is most likely? And you're right; I should have pointed that out initially (even though it was before the election, I could have used 2008 figures).
Yes, of course I meant most likely. Duh. I've edited my comment for the benefit of our thousands of future readers.