Sleeping beauty awakened: New odds at the dawn of the new day

Analysis 64 (1):10–21 (2004)
1. The story of Sleeping Beauty is set forth as follows by Dorr (2002): Sleeping Beauty is a paradigm of rationality. On Sunday she learns for certain that she is to be the subject of an experiment. The experimenters will wake her up on Monday morning, and tell her some time later that it is Monday. When she goes back to sleep, they will toss a fair coin. If the outcome of the toss is Heads, they will do nothing. If the outcome is Tails, they will administer a drug whose effect is to destroy all memories from the previous day, so that when she wakes up on Tuesday, she will be unable to tell [1] that it is not Monday. (2002: 292) Let HEADS be the hypothesis that the coin lands heads, and let TAILS be the hypothesis that it lands tails. The Sleeping Beauty Problem is this. When Sleeping Beauty finds herself awakened by the experimenters, with no memory of a prior awakening and with no ability to tell whether or not it is Monday, what probabilities should she assign to HEADS and TAILS respectively? Elga (2000) maintains that when she is awakened, P(HEADS) = 1/3 and P(TAILS) = 2/3. He offers the following intuitively plausible argument (2000: 143 4). If the experiment were performed many times, then over the long run about 1/3 of the awakenings would happen on trials in which the coin lands heads, and about 2/3 on trials in which it lands tails. So in the present circumstance in which the experiment is performed just once, P(HEADS) = 1/3 and..
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