# multifoliaterose comments on Why We Can't Take Expected Value Estimates Literally (Even When They're Unbiased) - Less Wrong

67 18 August 2011 11:34PM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Sort By: Best

Comment author: 18 August 2011 09:55:34PM *  1 point [-]

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.

Comment author: 18 August 2011 10:11:32PM 6 points [-]

It's intuitively plausible that a Solomonoff type prior would (at least approximately) yield such an assumption.

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.

Comment author: 18 August 2011 10:50:30PM *  0 points [-]

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.

Comment author: 19 August 2011 04:24:27AM *  2 points [-]

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.

Comment author: 19 August 2011 04:31:48AM 0 points [-]

Care to elaborate or give a reference?

Comment author: 19 August 2011 04:34:42AM *  0 points [-]
Comment author: 19 August 2011 04:50:57AM 0 points [-]

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!

Comment author: 19 August 2011 06:11:49PM 2 points [-]

Observations would merely shrink the tails by a multiplicative constant, they would not change the shape.