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Proper scoring rules for general decision models

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  • Chambers, Christopher P.

Abstract

If a decision maker whose behavior conforms to the max-min expected utility model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there is a scoring rule inducing the agent to announce that prior. We also show that on the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors).

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  • Chambers, Christopher P., 2008. "Proper scoring rules for general decision models," Games and Economic Behavior, Elsevier, vol. 63(1), pages 32-40, May.
    • Handle: RePEc:eee:gamebe:v:63:y:2008:i:1:p:32-40
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    Cited by:

    1. Bose, Subir & Daripa, Arup, 2023. "Eliciting second-order beliefs," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    2. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    3. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    4. Bose, Subir & Daripa, Arup, 2022. "Eliciting ambiguous beliefs using constructed ambiguous acts: Alpha-maxmin," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    5. Patrick Schmidt, 2019. "Eliciting ambiguity with mixing bets," Papers 1902.07447, arXiv.org, revised Aug 2024.
    6. Arthur Carvalho & Stanko Dimitrov & Kate Larson, 2018. "On proper scoring rules and cumulative prospect theory," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 343-376, November.
    7. Tsakas, Elias, 2018. "Robust scoring rules," Research Memorandum 023, Maastricht University, Graduate School of Business and Economics (GSBE).
    8. Chambers, Christopher P. & Healy, Paul J. & Lambert, Nicolas S., 2019. "Proper scoring rules with general preferences: A dual characterization of optimal reports," Games and Economic Behavior, Elsevier, vol. 117(C), pages 322-341.

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