https://en.m.wikipedia.org/wiki/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.
Resolves based on the consensus position of academic philosophers once a supermajority consensus is established. Close date extends until a consensus is reached.
References
Self-locating belief and the Sleeping Beauty problem, Adam Elga (2000) - https://www.princeton.edu/~adame/papers/sleeping/sleeping.pdf
Sleeping Beauty: Reply to Elga, David Lewis (2001) - http://www.fitelson.org/probability/lewis_sb.pdf
Sleeping Beauty and Self-Location: A Hybrid Model, Nick Bostrom (2006) - https://ora.ox.ac.uk/objects/uuid:44102720-3214-4515-ad86-57aa32c928c7/
The End of Sleeping Beauty's Nightmares, Berry Groissman (2008) - https://arxiv.org/ftp/arxiv/papers/0806/0806.1316.pdf
Putting a Value on Beauty, Rachael Briggs (2010) - https://joelvelasco.net/teaching/3865/briggs10-puttingavalueonbeauty.pdf
Imaging and Sleeping Beauty: A case for double-halfers, Mikaël Cozic (2011) - https://www.sciencedirect.com/science/article/pii/S0888613X09001285
Bayesian Beauty, Silvia Milano (2022) - https://link.springer.com/article/10.1007/s10670-019-00212-4
Small print
I will use my best judgement to determine consensus. Therefore I will not bet in this market. I will be looking at published papers, encyclopedias, textbooks, etc, to judge consensus. Consensus does not require unanimity.
If the consensus answer is different for some combination of "credence", "degree of belief", "probability", I will use the answer for "degree of belief", as quoted above.
Similarly if the answer is different for an ideal instrumental agent vs an ideal epistemic agent, I will use the answer for an ideal epistemic agent, as quoted above.
If the answer depends on other factors, such as priors or axioms or definitions, so that it could be 1/3 or it could be something else, I reserve the right to resolve to, eg, 50%, or n/a. I hope to say more after reviewing papers in the comments.
1,000