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There are 100 million votes, one of which decided the election (the N+1'th vote on the winning side, assuming N votes on the losing side).

If you prefer, you can play with binomial distributions to calculate P(side X wins with N votes && side X wins with N-1 votes) [1]. Using the normal approximation and ignoring the normalization prefactor (an overestimate) exp[(n(p-0.5)^2 / 1(np(1-p))] odds of having your vote matter. For p=0.501 (i.e., voters are split 50.1%, 49.9%), that works out to about 10^{-87}. For p=0.51, double floats are incapable of representing a number that small.

I stand by my statement. Your vote doesn't matter.

[1] Conceptually, this is slightly different from computing the odds that you cast the deciding vote, but I realize it is more useful from a decision theoretic perspective.




There's no point in putting it to "hard numbers" if you make terribly impractical guesstimates.


Please explain which of my approximations you believe changes my results significantly.

(By "significantly", I mean "increases the odds of your vote mattering to a number greater than, say, 10^{-86}. )


I can't help you clean up the calculations because the entire premise that the probability of "your vote mattering" times your potential financial gain from one candidate over another gives any reasonable estimate of utility of a vote is absurd.


It doesn't have to be financial gain - it can be altruistic gain from policy choices. As I said in another post, if you personally would be willing to spend $50k to legalize gay marriage (for example), you can replace $50k of financial gain by $50k worth of utility derived from helping others.




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