Teddy Seidenfeld: Sleeping Beauty’s Credences

The Sleeping Beauty problem has spawned a long debate between Thirders and Halfers which centers on their conflicting answers to the question “What is Sleeping Beauty’s credence in the event that the coin lands Heads?” In this paper, we show that the conflicting answers that Thirders and Halfers provide are the results of conflicting assumptions that each group makes. We lay out those assumptions (some implicit, some explicit, some plausible, some less plausible) and embed them into a general framework which allows a form of reconciliation between the conflicting answers by making it explicit which assumptions are used to reach each conclusion. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the Experiment. The same principle also allows for modeling more familiar cases of forgetting while highlighting how the more familiar cases differ from Sleeping Beauty. In addition, we explore what fair prices Sleeping Beauty should compute for various gambles that she might be offered during the experiment and how these relate to her credences.

Teddy Seidenfeld is Professor of Philosophy and Statistics at Carnegie Mellon University. He works on foundations at the interface between philosophy and statistics, often being concerned with problems that involve multiple decision makers. For example, in collaboration with M.J. Schervish and J.B. Kadane (Statistics, CMU), they relax the norms of Bayesian theory to permit a unified standard, both for individuals acting as separate decision makers and collectively, in forming a cooperative group agent. By contrast, this is an impossibility for strict Bayesian theory.