Silvia Milano (University of Oxford)
The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments.I show that, contrary to what is commonly accepted in the literature, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the solution satisfies all the standard Bayesian principles, including Conditionalization and Reflection, is immune from Dutch Books, and does not make any appeal to the Restricted Principle of Indifference which, I argue, is incompatible with the essential features of Bayesian reasoning. Moreover, it emerges from my discussion that the disagreement between different solutions proposed in the literature is not due to the inapplicability of Bayesianism to centered settings, but is instead an instance of the familiar problem of setting the priors.
