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multifoliaterose comments on Why We Can't Take Expected Value Estimates Literally (Even When They're Unbiased) - Less Wrong
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Approximately normal distributions arise from the assumption of the involvement of many independent random variables with the largest ones being of roughly comparable size. It's intuitively plausible that a Solomonoff type prior would (at least approximately) yield such an assumption.
Intuitively plausible, but wrong; Solomonoff priors have long, very slowly decreasing tails.
Care to elaborate or give a reference?
See http://lesswrong.com/lw/6fd/observed_pascals_mugging/4fky and the replies.
Okay, I didn't mean a literal Solomonoff prior; I meant "what your posterior would be after starting with a Solomonoff prior, observing the natural/human world at some length and Bayesian updating accordingly." The prior alone contains essentially no information!
Observations would merely shrink the tails by a multiplicative constant, they would not change the shape.
But even if "intuitively plausible" equates to, say, 0.9999 probability, that's insufficient to disarm Pascal's Mugging. I think there's at least 0.0001 chance that a better approximate prior distribution for "value of an action" is one with a "heavy tail", e.g., one with infinite variance.
Sure, the present post deals only with the case where the value that one assigns to an action obeys a (log)-normal distribution over actions. In the case that you describe, there may (or may not) be a different way to disarm Pascal Mugging.