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Jonathan_Graehl comments on Fundamentals of kicking anthropic butt - Less Wrong
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I really like your explanations in this thread.
However, I've always had the feeling that people raising "it just depends on the utility function / bet / payoff" were mostly trying to salve egos wounded by having wrongly analyzed the problem. It's instructive to consider utility, but don't pretend to be confused about whether Beauty should be surprised to learn that the toss was H and not T.
You're right. For that reason, I think my explanations in the follow-up comments were better than this first attempt (not that this post is incorrect, it just doesn't quite address the main point). I've previously tried to say the same thing here and here. The opinion I have hasn't changed, but maybe my way of expressing it has.