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Uncertainty and Compound Lotteries: Calibration

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Halevy, Yoram
Ozdenoren, Emre

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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. Recent 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 evaluation of the corresponding compound objective lottery. Calibration provides the foundation that allows one to formalize and understand the tight empirical association between probabilistic sophistication and reduction of compound lotteries, for all two-stage probabilistically sophisticated preferences.

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Paper provided by Microeconomics.ca Website in its series Micro Theory Working Papers with number yoram_halevy-2008-7.

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Length: 29 pages
Date of creation: 17 Jun 2008
Date of revision: 17 Jun 2008
Handle: RePEc:ubc:pmicro:yoram_halevy-2008-7

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

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  6. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003. [Downloadable!]
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