Note to Self: Apropos of the Sleeping Beauty Problem: Adam Elga: Self-Locating Belief and the Sleeping Beauty Problem...
There are three π here:
- π1: a parameter of nature that describes the probability that the coin, when tossed, will come up heads: π1 = 1/2
- π2: 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: π1 = 1/3
- π3: 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?": π3 = 1/2
Which of these π1, π2, π3 is the "right" answer Sleeping Beauty should give?