The Sleeping Beauty problem

Question

On Sunday, Beauty agrees to the following experiment and is put to sleep. A fair coin is flipped.

If it lands heads, she is woken on Monday, interviewed, and the experiment ends.
If it lands tails, she is woken on Monday, interviewed, put back to sleep with her memory of the Monday waking erased, then woken again on Tuesday and interviewed.

Each time she is woken she is asked: "What is your credence (degree of belief) that the coin landed heads?" She knows all these rules and cannot tell which day it is.

What should she answer? Give the case for each of the two standard answers and explain what the disagreement is really about.

Accepted Answer

The two camps answer 1/3 ("thirders") and 1/2 ("halfers"), and the dispute has not been settled; it turns on what a probability is supposed to measure when the same person can exist at several indistinguishable moments. The thirder argument (1/3). Run the experiment many times. Half the runs are heads, with one waking each; half are tails, with two wakings each. Of all the wakings, one third are heads-wakings and two thirds are tails-wakings. Each waking feels identical from the inside, so on any given waking the odds are 2 to 1 that it is a tails-waking: credence in heads should be 1/3. A be…

The Sleeping Beauty problem

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