On the Interpretation of Decision Problems the beauty experiment pdf Imperfect Recall” where the “paradox of the absent minded driver” was first introduced and the Sleeping Beauty problem discussed as Example 5. On Sunday she will be put to sleep.
Once or twice, during the experiment, Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. Beauty will be awakened and interviewed on Monday only. If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday. In either case, she will be awakened on Wednesday without interview and the experiment ends. Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. This problem continues to produce ongoing debate.
Suppose Sleeping Beauty is told and she comes to fully believe that the coin landed tails. Monday should equal her credence that it is Tuesday since being in one situation would be subjectively indistinguishable from the other. Consider now that Sleeping Beauty is told upon awakening and comes to fully believe that it is Monday. She knows the experimental procedure doesn’t require the coin to actually be tossed until Tuesday morning, as the result only affects what happens after the Monday interview. Since these three outcomes are exhaustive and exclusive for one trial, the probability of each is one-third by the previous two steps in the argument. Sleeping Beauty receives no new non-self-locating information throughout the experiment because she is told the details of the experiment. 2 since she gains no new relevant evidence when she wakes up during the experiment.