On the representation of incomplete preferences under uncertainty with indecisiveness in tastes and beliefs

Recently, there has been some interest on models of incomplete preferences under uncertainty that allow for incompleteness due the multiplicity of tastes and beliefs. In particular, Galaabaatar and Karni (Econometrica 81(1):255–284, 2013 ) work with a strict partial order and present axiomatizations of the Multi-prior Expected Multi-utility and the Single-prior Expected Multi-utility representations. In this paper, we characterize both models using a preorder as the primitive. In the case of the Multi-prior Expected Multi-utility representation, like all the previous axiomatizations of this model in the literature, our characterization works under the restriction of a finite prize space. In our axiomatization of the Single-prior Expected Multi-utility representation, the space of prizes is a compact metric space. Later in the paper, we present two applications of our characterization of the Single-prior Expected Multi-utility representation and discuss the necessity of an axiomatization of the Multi-prior Expected Multi-utility model when the prize space is not finite. In particular, we explain how the two applications we develop in this paper could be generalized to that model if we had such an axiomatization. Copyright Springer-Verlag Berlin Heidelberg 2015