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Bets on Hats: On Dutch Books Against Groups, Degrees of Belief as Betting Rates, and Group-Reflection


The Story of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable.

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L. Bovens 1995. “P and I Will Believe that not-P’: Diachronic Constraints on Rational Belief.Mind 104: 737–60.

L. Bovens and W. Rabinowicz . 2010. “The Puzzle of the Hats.Synthese 172: 5778.

D. Christensen 1991. “Clever Bookies and Coherent Beliefs.The Philosophical Review 100: 229–47.

R. Selten 1975. “A Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games.International Journal of Game Theory 4: 2555.

B. van Fraassen 1984. “Belief and the Will.Journal of Philosophy 81: 235–56.

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  • ISSN: 1742-3600
  • EISSN: 1750-0117
  • URL: /core/journals/episteme
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