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A Dutch-Book Trap for Misspecification

Emiliano Catonini,Giacomo Lanzani

Published 2022 in Unknown venue

ABSTRACT

We provide Dutch-book arguments against misspecified Bayesian learning. An agent progressively learns about a state and is offered a bet after every discovery. We say the agent is deterministically Dutch-booked when they would accept all bets, but their payoff is ex-post negative under each state. More generally, we say that the agent is Dutch-booked when they would accept all bets, but their expected payoff under each fundamental state is negative. With this, the agent cannot be deterministically Dutch-booked if and only if they update their beliefs using Bayes'rule, even with misspecified likelihoods. The agent cannot be Dutch booked if and only if they update their beliefs using Bayes'rule with a lexicographic prior and using the correct data-generating process. We show that offers of financial instruments and behavior in Monty Hall problems can be viewed as Dutch books that extract a sure expected gain from a misspecified population.

PUBLICATION RECORD

  • Publication year

    2022

  • Venue

    Unknown venue

  • Publication date

    2022-02-21

  • Fields of study

    Philosophy, Economics

  • Identifiers
    arXiv 2202.10121
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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