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Manfred comments on Fundamentals of kicking anthropic butt - Less Wrong
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Easy solution for the Sleeping Beauty problem: instead of merely asking her her subjective probability, we can ask her to bet. The question now becomes "at what odds would you be willing to bet?". So here are the possibilities:
Heads or tails comes up with equal probability (0.5). But when it comes up Tails, the stakes double (because she will bet twice). So, what will generate the correct bets is the assumption that Tails will subjectively come up 2/3 of the time.
I know it looks cheap, because it doesn't answer the question "But what really is the subjective probability?". I don't know, but I'll find a way to make the correct decision anyway.
I don't think using betting is cheap at all, if you want to answer questions about decision-making. But I still wanted to answer the question about probability :D