Uncertainty and Compound Lotteries: Calibration

Yoram Halevy and Emre Ozdenoren

Working Papers from University of Toronto, Department of Economics

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.

Keywords: ambiguity; probabilistic sophistication; reduction of compound lotteries; Ellsberg (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
Pages: Unknown pages
Date: 2021-11-18
New Economics Papers: this item is included in nep-exp and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Uncertainty and compound lotteries: calibration (2022)
Working Paper: Uncertainty and Compound Lotteries: Calibration (2008)
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