Do bets reveal beliefs?
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This paper examines the preference-based approach to the identification of beliefs. It focuses on the main problem to which this approach is exposed, namely that of state-dependent utility. First, the problem is illustrated in full detail. Four types of state-dependent utility issues are distinguished. Second, a comprehensive strategy for identifying beliefs under state-dependent utility is presented and discussed. For the problem to be solved following this strategy, however, preferences need to extend beyond choices. We claim that this a necessary feature of any complete solution to the problem of state-dependent utility. We also argue that this is the main conceptual lesson to draw from it. We show that this lesson is of interest to both economists and philosophers.
KeywordsBeliefs Subjective probability State-dependent utility Hypothetical preferences Revealed preference
The author thanks the Editor-in-Chief Wiebe van der Hoek, two referees, Mikaël Cozic, Éric Danan, Vincent Éli, Itzhak Gilboa, Raphaël Giraud, Brian Hill, Marcus Pivato, Fanyin Zheng and especially Philippe Mongin for most helpful comments and discussions. The author is sole responsible for all remaining errors or omissions. Research for this paper was funded by the Université de Cergy-Pontoise, and before that by the École Normale Supérieure - Ulm (grants ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL*).
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