Abstract
A decision problem under uncertainty is often given with a piece of objective but imprecise information about the states of the world such as in the Ellsberg urn. By incorporating such information into the smooth ambiguity model of Seo [35], we characterize a class of smooth ambiguity representations whose second-order beliefs are consistent with the objective information. As a corollary, we provide an axiomatization for the second-order expected utility, which has been studied by Nau [28], Neilson [30], Grant, Polak, and Strzalecki [16], Strzalecki [37], and Ghirardato and Pennesi [11]. In our model, attitude toward uncertainty can be disentangled from a perception about uncertainty and connected with attitude toward reduction of compound lotteries.
