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Oscar_Cunningham comments on Why We Can't Take Expected Value Estimates Literally (Even When They're Unbiased) - Less Wrong
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I'm afraid that I don't remember the details of the paper I linked to above, you'll have to look at it to see why they don't consider that a valid distribution (perhaps because the things that the mugger says have to be counted as evidence, and this can't decrease that quickly for some reason? I'm afraid I don't remember.)