Sleeping Beauty and the forgetful Bayesian
1. Consider the case of Sleeping Beauty: on Sunday she is put to sleep, and she knows that on Monday experimenters will wake her up, and then put her to sleep with a memory-erasing drug that causes her to forget that waking-up. The researchers will then flip a fair coin; if the result is Heads, they will allow her to continue to sleep, and if the result is Tails, they will wake her up again on Tuesday. Thus, when she is awakened, she will not know whether it is Monday or Tuesday. On Sunday, she assigns probability 1/2 to the proposition H that the coin lands Heads. What probability should she assign to H on Monday, when she wakes up? Adam Elga (2000) argues that the answer is 1/3. As Elga (citing Ned Hall) points out, though, this answer violates Bas van Fraassen's (1984, 1995a) Reflection Principle, which entails that