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Uncertainty and Compound Lotteries: Calibration

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  • Yoram Halevy
  • Emre Ozdenoren

Abstract

The Ellsberg experiments provide an intuitive illustration that the Savage approach, which reduces subjective uncertainty to risk, is not rich enough to capture many decision makers' preferences. Experimental evidence suggests that decision makers reduce uncertainty to compound risk. This work presents a theoretical model of decision making in which preferences are defined on both Savage subjective acts and compound objective lotteries. Preferences are two-stage probabilistically sophisticated when the ranking of acts corresponds to a ranking of the respective compound lotteries induced by the acts through the decision maker's subjective belief. This family of preferences includes various theoretical models that have been proposed in the literature to accommodate non-neutral attitude towards ambiguity. The principle of calibration, which was used by Ramsey and de Finetti, allows an outside observer to relate preferences over acts and compound objective lotteries. If preferences abide by the calibration axioms, the evaluation of the compound lottery induced by an act through the subjective belief coincides with the valuation of the corresponding compound objective lottery. Calibration provides a foundation to formalize and understand the tight empirical association between probabilistic sophistication and reduction of compound lotteries, for all two-stage probabilistically sophisticated preferences.

Suggested Citation

  • Yoram Halevy & Emre Ozdenoren, 2021. "Uncertainty and Compound Lotteries: Calibration," Working Papers tecipa-713, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-713
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    Cited by:

    1. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    2. Mohammed Abdellaoui & Peter Klibanoff & Lætitia Placido, 2015. "Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity," Management Science, INFORMS, vol. 61(6), pages 1306-1322, June.
    3. Heydari, Pedram, 2024. "Regret, responsibility, and randomization: A theory of stochastic choice," Journal of Economic Theory, Elsevier, vol. 217(C).
    4. Ozgur Evren, 2024. "Second-Order Representations: A Bayesian Approach," Working Papers w0291, New Economic School (NES).
    5. Jianjun Miao, 2022. "Introduction to the special issue in honor of Larry Epstein," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 329-333, September.
    6. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    7. Roxane Bricet, 2018. "The price for instrumentally valuable information," THEMA Working Papers 2018-10, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    8. Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.

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    More about this item

    Keywords

    ambiguity; probabilistic sophistication; reduction of compound lotteries; Ellsberg;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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