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Rune comments on Open Thread: March 2010 - Less Wrong
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Say Omega appears to you in the middle of the street one day, and shows you a black box. Omega says there is a ball inside which is colored with a single color. You trust Omega.
He now asks you to guess the color of the ball. What should your probability distribution over colors be? He also asks for probability distributions over other things, like the weight of the ball, the size, etc. How does a Bayesian answer these questions?
Is this question easier to answer if it was your good friend X instead of Omega?
See also.
Thanks!
I don't know about "should", but my distribution would be something like
red=0.24 blue=0.2 green=0.09 yellow=0.08 brown=0.04 orange=0.03 violet=0.02 white=0.08 black=0.08 grey=0.02 other=0.12
Omega knows everything about human psychology and phrases it's questions in a way designed to be understandable to humans, so I'm assigning pretty much the same probabilities as if a human was asking. If it was clear that white black and grey are considered colors their probability would be higher.
See http://wiki.lesswrong.com/wiki/I_don%27t_know