On my Manifold Survey, I will ask:

What is the answer to the Sleeping Beauty problem?

Sleeping Beauty agrees to undergo an experiment and is told the following details: On Sunday, a fair coin will be flipped, but she won't be told the results. She will then be given a drug that puts her to sleep until Wednesday. If the coin lands heads, she will be woken up once on Monday and asked how likely it is (specifically, what her credence is) that the coin landed heads. She will then take the drug again, which also induces amnesia so that she forgets the interview, and sleep until Wednesday. If the coin lands tails, she will be woken twice, once on Monday and once on Tuesday, to be asked the same question, before taking the drug again each time. When she is interviewed, she won't be told what day is it, and because she took the drug, she won't remember the previous interviews. Suppose Sleepy Beauty is an ideally rational agent and has just been woken up for an interview: What should her credence be that the coin landed heads, and what should her credence be that it is Tuesday?

• 1/3 chance that the coin landed heads, 1/3 chance that it is Tuesday

• 1/2 chance that the coin landed heads, 1/4 chance that it is Tuesday

• 1/2 chance that the coin landed heads, 1/2 chance that it is Tuesday

• 1/4 chance that the coin landed heads, 1/2 chance that it is Tuesday

• The problem is ambiguous, so there is no unique correct answer.

• Other

• Not sure

Only counting respondents who select one of the first four options, what will the plurality say is the probability that the coin landed heads? This means that the second and third option are being grouped together here.

The close date of this question may change depending on when I decide to run the survey. See Plasma's Manifold Survey for other questions about the survey.