Say that the second time you wake her on Monday, you just outright ignore everything she says. Suddenly, because you changed your behavior, her objectively correct belief is 0.5 / 0.5?
The real problem is that the question is undefined—Sleeping Beauty has no goal function. If she had a goal function, she could just choose the probability assignment that maximized the payoff under it. All the handwaving at “standard frameworks” is just another way to say “assignment that maximizes payoff under a broad spread of goals”.
Alternate scenario: all three wakings of Sleeping Beauty are actually copies. Monday 2 is deleted after a few minutes. What’s the “true” probability then?
Say that the second time you wake her on Monday, you just outright ignore everything she says. Suddenly, because you changed your behavior, her objectively correct belief is 0.5 / 0.5?
The real problem is that the question is undefined—Sleeping Beauty has no goal function. If she had a goal function, she could just choose the probability assignment that maximized the payoff under it. All the handwaving at “standard frameworks” is just another way to say “assignment that maximizes payoff under a broad spread of goals”.
Alternate scenario: all three wakings of Sleeping Beauty are actually copies. Monday 2 is deleted after a few minutes. What’s the “true” probability then?