Objective rationality and uncertainty averse preferences

Abstract

As in [Gilboa et al.., 2010], we consider a decision maker characterized by two binary relations: ≿* and ≿∧. The first binary relation is a Bewley preference. It models the rankings for which the decision maker is sure. The second binary relation is an uncertainty averse preference, as defined by [Cerreia-Vioglio et al.., 2011c]. It models the rankings that the decision maker expresses if he has to make a choice. We assume that ≿∧ is a completion of ≿*. We identify axioms under which the set of probabilities and the utility index representing ≿* are the same as those representing ≿∧. In this way, we show that Bewley preferences and uncertainty averse preferences, two different approaches to modelling decision making under Knightian uncertainty, are complementary. As a by-product, we extend the main result of [Gilboa et al.., 2010], who restrict their attention to maxmin expected utility completions.

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