The Sleeping Beauty paradox is a problem about conditional probability and self-locating belief. On Sunday, a fair coin is tossed. If it lands heads, Sleeping Beauty is awakened on Monday only. If it lands tails, she is awakened on Monday and Tuesday, with her memory of the Monday awakening erased before Tuesday. Whenever she awakens, she is asked for the probability that the coin landed heads (Elga 2000, Bischoff 2023).
"Halfers" answer 
, reasoning that awakening supplies no new non-self-locating
evidence about the fair coin (Lewis 2001). "Thirders"
answer 
,
treating the three possible awakening situations--heads on Monday, tails on Monday,
and tails on Tuesday--as equally weighted from Beauty's perspective (Elga 2000).
The disagreement concerns how to update probabilities
when an observer knows that the observation protocol makes some outcomes produce
more indistinguishable observations than others. Closely related variants can have
different answers if the question, sampling procedure, or betting payoff is changed
(Winkler 2017).
