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I don't understand how the author's estimate is justified. He wants to take the probability that the margin is within 2 million and then divide by two million? Maybe he is appealing to some limiting argument? But we are presumably dealing with a discrete random variable.

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I think the algorithm he is suggesting is..

1. Get empirical probability vote is within 2 million from previous N elections. (so, 1 if it is within 2 mill, and 0 of not, then average). Use it as p(vote is within 2 million). 2. Assume that if a vote is within 2 million, then the exact number of votes is uniform between 0 and 2 million. Then, the probability of a tie, given that the vote is within 2 million is p(vote within w million) / 2 million.

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