# Perplexed comments on Non-trivial probability distributions for priors and Occam's razor - Less Wrong

2 11 January 2011 03:59AM

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Comment author: 11 January 2011 04:25:01PM 0 points [-]

I must be missing something. Your argument makes no sense at all to me. It is very simple to construct a countable set of hypotheses of various lengths, all of which have prior probability exactly 1/2. The hypotheses denote events in a universe consisting of an infinite sequence of coin flips, for example.

Furthermore, I must be misreading your definition of h(n), because as I read it, h(n) goes to 1 as n goes to infinity. I.e. it becomes overwhelmingly likely that at least one shorter-than-n hypothesis is correct.

Comment author: 11 January 2011 07:10:31PM *  0 points [-]

I must be missing something. Your argument makes no sense at all to me. It is very simple to construct a countable set of hypotheses of various lengths, all of which have prior probability exactly 1/2. The hypotheses denote events in a universe consisting of an infinite sequence of coin flips, for example.

Hypotheses in this sense are exclusive. If you prefer, consider hypotheses to be descriptors of all possible data one will get from some infinite string of bits.

Furthermore, I must be misreading your definition of h(n), because as I read it, h(n) goes to 1 as n goes to infinity. I.e. it becomes overwhelmingly likely that at least one shorter-than-n hypothesis is correct.

Sorry, yes, h(n) should be for statements with length at least n not at most n.

Comment author: 11 January 2011 05:14:53PM *  0 points [-]

Insert "mutually exclusive" where appropriate :D

Yes, the argument is confused, but I think that's only the writing, not the idea. I think this may not be as general as it could be, though - it would be nice if Occam's razor applied for other conditions.

Oh, wait - it doesn't quite work. I should probably write my own reply for that bit.