Self-Locating Belief and the Sleeping Beauty Problem Once Again...

Note to Self: Apropos of the Sleeping Beauty Problem: Adam Elga: Self-Locating Belief and the Sleeping Beauty Problem...

There are three �� here:

��1: a parameter of nature that describes the probability that the coin, when tossed, will come up heads: ��1 = 1/2
��2: a number that Sleeping Beauty should keep in mind when deciding at what odds to bet that the coin came up heads if she wants to make money: ��1 = 1/3
��3: a number that Sleeping Beauty should tell a third party who asks her: "I'm going to make one and only one bet this week as to how this coin came out. What number should I have in mind in deciding at what odds to take heads if I want to make money?": ��3 = 1/2

Which of these ��1, ��2, ��3 is the "right" answer Sleeping Beauty should give?

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