Sleeping beauty and the current chance evidential immodest dominance axiom

Abstract

Concerning the notorious Sleeping Beauty problem, philosophers have debated whether 1/2 or 1/3 is rational as Beauty's credence in (H) the coin's landing heads. According to Kierland and Monton, the answer depends on whether her goal is to minimize average or total inaccuracy because, while the expected average inaccuracy of Halfing (i.e., assigning 1/2 to H) is smaller than that of Thirding (i.e., assigning 1/3 to H), the expected total inaccuracy of Thirding is lower than that of Halfing. In this paper, I argue that Halfing is average accuracy dominated but Thirding is not; and that each of the standard forms of Halfing and Thirding regards a different credence assignment as better than itself in terms of total accuracy. Therefore, Halfing is irrational, and Thirding is likely to be rational, for the goal of minimizing average inaccuracy; but both Halfing and Thirding, at least in their standard forms, are irrational for the goal of minimizing total inaccuracy.