Sleeping Beauty’s Credences
نویسندگان
چکیده
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.
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