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khafra comments on Why We Can't Take Expected Value Estimates Literally (Even When They're Unbiased) - Less Wrong
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I'm not so sure. Do you mean (3.2 lives|pi lives) to log(3^^^3) digits of precision? If you don't, I think it misleads intuition to think about the probability of an action saving 3.2 lives, to two decimal places; vs. pi lives, to indefinite precision.
I can't think of any right now, but I feel like if I really put my creativity to work for long enough, I could think of more ways to save 3.14159265358979323846264 lives than 3.20000000000000000000000 lives.
I meant 3.2 lives to arbitrary precision vs. pi lives to arbitrary precision. Anyway, my point was that there's going to be some deviation from a log-normal distribution on account of contingent features of the universe that we live in (mathematical, physical, biological, etc.) but that probably a log-normal distribution is a closer approximation to the truth than what one would hope to come up with a systematic analysis of the complexity of the numbers involved.