On the indifference relation in Bewley preferences

Bewley’s (2002) influential model of preferences over uncertain prospects features an incomplete preference relation and a set of priors over the states of the world such that one act is preferred to another if and only if its expected utility is higher under every prior in that set. This note shows that, under general conditions on preferences, the decision maker in the Bewley model cannot be indifferent between distinct monetary acts whenever the set of priors is fully-dimensional. In the special case of two states, in particular, such “objectively rational” preferences are incomplete if and only if the indifference relation is trivial in the above sense.