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Sniffnoy comments on Why We Can't Take Expected Value Estimates Literally (Even When They're Unbiased) - Less Wrong
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I wouldn't expect there to be one -- though you could always use 1/2 -- but the original requirement is not for a confidence level but for a way of generating a total ordering. I.e. the arbitrariness is that you have a free parameter in the first place, not so much the choice of it. That's what makes it a free parameter, really!