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The Impossibility of Compromise: Convexity and Uniqueness in Decision Making under Risk and Uncertainty

Ghirardato, Paolo and Marinacci, Massimo (1999) The Impossibility of Compromise: Convexity and Uniqueness in Decision Making under Risk and Uncertainty. Social Science Working Paper, 1055. California Institute of Technology , Pasadena, CA. (Unpublished)

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The main set of results of the paper shows that for expected utility preferences, agreement of two preferences on one (non-extreme) indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences under uncertainty, in both Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) frameworks. For these two frameworks, we present an analogous result for beliefs, showing that if two decision makers agree on a likelihood indifference class, they must have identical probabilities. The second part of the paper shows two different sets of consequences of the uniqueness results. First, we study the preference aggregation results of the type pioneered by Harsanyi. We show that under the assumptions of those results, the existence of a weak form of agreement among the agents implies that all their preferences are identical. Then, we study the models which extend expected utility to incorporate ambiguity aversion, and show that for a class of these models a very weak condition is surprisingly equivalent to expected utility maximizing behavior.

Item Type:Report or Paper (Working Paper)
Additional Information:This paper subsumes an earlier note circulated with the title "Convex-Rangedness in Decision Making with Additive and Non-Additive Beliefs." We thank Kim Border, Itzhak Gilboa, Matt Jackson, Philippe Mongin, and Peter Wakker for helpful comments and discussions. Part of this paper was written while the second author was with the Department of Economics at the University of Toronto, and part while we were guests of the Istituto di Metodi Quantitativi of the Universita Bocconi (Milano, Italy). Marinacci is grateful to the Social Sciences and Humanities Research Council of Canada for financial support.
Group:Social Science Working Papers
Funding AgencyGrant Number
Social Sciences and Humanities Research Council of Canada (SSHRC)UNSPECIFIED
Subject Keywords:Subjective Expected Utility, Uniqueness, Range Convexity, Preference Aggregation, Ambiguity Averse Preferences
Series Name:Social Science Working Paper
Issue or Number:1055
Classification Code:JEL: D81
Record Number:CaltechAUTHORS:20170810-164741187
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80267
Deposited By: Jacquelyn Bussone
Deposited On:11 Aug 2017 19:05
Last Modified:03 Oct 2019 18:29

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