Sleeping Beauty: theme and variations

Sleeping Beauty theme Sleeping Beauty, before she goes to sleep on Sunday, knows that she is the subject of the following experiment: A fair coin will be tossed; if it lands showing heads, she will be awakened Monday morning. If the coin lands showing tails, she will be awakened Monday morning, will be put to sleep Monday evening with a drug which causes her to forget everything she experienced on Monday, and will be awakened a second time on Tuesday morning. Since on Tuesday morning she will have no recollection of Monday, Tuesday morning and Monday morning will be indistinguishable for her, and so (whichever way the coin lands) when she wakes she will not know whether it is Monday or Tuesday. This story was published by Elga (2000) to pose the following question: when Sleeping Beauty wakes, what should be her credence that the coin landed showing heads? Elga, and a majority of the participants in the ensuing discussion (“thirders”) claim that the answer is one-third (quickly, because if this experiment were run a large number of times, the expected fraction of awakenings with the coin showing heads would be one-third), but others, e.g. David Lewis (2001) (“halfers”) argue that the answer is one-half (quickly, because when she wakes she will know exactly as much as she did on Sunday evening, when her credence for Heads was surely one-half). In this paper,