Objective Rationality and Uncertainty Averse Preferences

As in Gilboa, Maccheroni, Marinacci, and Schmeidler [12], we consider a decision maker characterized by two binary relations: % and %^. The …rst 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 de…ned by Cerreia-Vioglio, Maccheroni, Marinacci, and Montrucchio [4]. 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 di¤erent approaches in modelling decision making under Knightian uncertainty, are complementary. As a by-product, we extend the main result of Gilboa, Maccheroni, Marinacci, and Schmeidler [12], who restrict their attention to maxmin expected utility completions. I would like to thank Itzhak Gilboa, Peter Klibano¤, Efe Ok, Ben Polak, David Schmeidler, Tomasz Strzalecki, the DTEA 2012 conference audience, and, especially, Pierpaolo Battigalli, Erio Castagnoli, Alejandro Francetich, Maria Kuecken, Fabio Maccheroni, and Massimo Marinacci for very helpful suggestions. I am also very grateful to the co–editor, Faruk Gul, and an anonymous referee for very insightful comments, which vastly improved the paper. Part of this research was done while I was visiting the Cowles Foundation at Yale University which I thank for its hospitality. The …nancial support of ERC (advanced grant BRSCDP–TEA) is gratefully acknowledged.