Sleeping Beauty problem

The Sleeping Beauty problem is a puzzle in decision theory in which whenever an ideally rational epistemic agent is awoken from sleep, they have no memory of whether they have been awoken before. Upon being told that they have been woken once or twice according to the toss of a coin, once if heads and twice if tails, they are asked their degree of belief for the coin having come up heads. History The problem was originally formulated in unpublished work in the mid-1980s by Arnold Zuboff (the work was later published as "One Self: The Logic of Experience") followed by a paper by Adam Elga. A formal analysis of the problem of belief formation in decision problems with imperfect recall was provided first by Michele Piccione and Ariel Rubinstein in their paper: "On the Interpretation of Decision Problems with Imperfect Recall" where the "paradox of the absent minded driver" was first introduced and the Sleeping Beauty problem discussed as Example 5. The name "Sleeping Beauty" was given to the problem by Robert Stalnaker and was first used in extensive discussion in the Usenet newsgroup rec.puzzles in 1999. The problem As originally published by Elga, the problem was: Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads? The only significant difference from Zuboff's unpublished versions is the number of potential wakings; Zuboff used a large number. Elga created a schedule within which to implement his solution, and this has become the canonical form of the problem: Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice, during the experiment, Sleeping Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake: If the coin comes up heads, Sleeping 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.