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A Dutch book argument for belief consistency

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  • Emiliano Catonini

Abstract

An agent progressively learns about a state of the world. A bookmaker is ready to offer one bet after every new discovery. I say that the agent is Dutch-booked when she is willing to accept every single bet, but her expected payoff is negative under each state, where the expected payoff is computed with the objective probabilities of different discoveries conditional on the state. I introduce a rule of coherence among beliefs after counterfactual discoveries that is necessary and sufficient to avoid being Dutch-booked. This rule characterizes an agent who derives all her beliefs with Bayes rule from the same Lexicographic Conditional Probability System (Blume, Brandenburger and Dekel, 1991).

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  • Emiliano Catonini, 2022. "A Dutch book argument for belief consistency," Papers 2202.10121, arXiv.org.
    • Handle: RePEc:arx:papers:2202.10121
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    References listed on IDEAS

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    1. Battigalli, P. & Catonini, E. & Manili, J., 2023. "Belief change, rationality, and strategic reasoning in sequential games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 527-551.
    2. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Pierpaolo Battigalli & Emiliano Catonini, 2022. "The Epistemic Spirit of Divinity," Working Papers 681, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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