Sleeping Beauty problem

Each time she will have no memory of whether she has been awoken before, and is asked what her degree of belief that “the outcome of the coin toss is Heads” ought to be when she is first awakened.

[4][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.

[6] A more recent paper by Peter Winkler discussing different sides of the problem was published in The American Mathematical Monthly in 2017.

A fair coin will be tossed to determine which experimental procedure to undertake: In either case, she will be awakened on Wednesday without interview and the experiment ends.

During the interview Sleeping Beauty is asked: "What is your credence now for the proposition that the coin landed heads?"

Adam Elga argued for this position originally[3] as follows: Suppose Sleeping Beauty is told and she comes to fully believe that the coin landed tails.

In the heads scenario, Sleeping Beauty would spend her wager amount one time, and receive 1 money for being correct.

David Lewis responded to Elga's paper with the position that Sleeping Beauty's credence that the coin landed heads should be 1/2.

Mikaël Cozic,[10] in particular, argues that context-sensitive propositions like "it is Monday" are in general problematic for conditionalization and proposes the use of an imaging rule instead, which supports the double halfer position.

This view asserts that the thirder and halfer positions are both correct answers, but to different questions.

[11][12][13] The key idea is that the question asked of Sleeping Beauty, "what is your credence that the coin came up heads", is ambiguous.