Ambiguity in the Context of Probabilistic Beliefs

Klaus Nehring

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Decision-Making and Behavioral Economics Economic and Environmental Valuation Experimental Behavioral Economics Studies

Abstract

When are a decision maker's preferences compatible with speci ed probabilistic beliefs? We propose two de nitions of \compatibility as possible answers to this question. The weaker one requires simply that the decision maker prefer to bet on an event whenever it is more likely. It is shown that under regularity conditions there exists a unique (incomplete) maximal comparative likelihood relation such that a given preference ordering is compatible with it. This relation yields a model-free notion of \revealed unambiguous beliefs; it implies a de nition of \revealed unambiguous events that is strictly more demanding than Epstein-Zhang (2001)'s. A stronger notion of compatibility called Tradeo® Consistency requires that the decision maker rank acts according to their expected utility whenever possible. Given \minimally probabilistic beliefs, Tradeo® Consistency entails a complete determination of preferences over multivalued acts by betting preferences and consequence utilities. Exluding all departures from expected utility maximization due to Allais-type probabilistic risk-aversion, it leads to a concept of \utility sophistication dual to Machina-Schmeidler's \probabilistic sophistication. We also propose two \Ellsbergian de nitions of ambiguity aversion in terms of betting preferences and characterize their close link to the major notions of ambiguity aversion proposed in the literature. ¤This version is still quite rough and incomplete; it is also clearly too long, and will most likely be split in future versions. Nonetheless, I would greatly appreciate any comments and suggestions. ye-mail: kdnehring@ucdavis.edu zSome of the main ideas of this paper were presented in December 1996 at LOFT2 in Torino, Italy, and in July 2001 at RUD in Venice, Italy. I am grateful to Juergen Eichberger, Paolo Ghirardato and Clemens Puppe for helpful comments.

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References

1961Risk, Ambiguity, and the Savage Axioms 1953Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine 2004Subjective probability and expected utility without additivity 1986Maxmin Expected Utility with a Non-Unique Prior 1992A More Robust Definition of Subjective Probability 2002Ambiguity Made Precise: A Comparative Foundation 1989Additive Representations of Preferences 2001Subjective Probabilities on Subjectively Unambiguous Events

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