In many situations a decision maker has incomplete psychological preferences, and the weak axiom of revealed preference (WARP) is often violated. In this paper we relax WARP, and replace it with convex axiom of revealed non-inferiority (CARNI). An alternative x is revealed inferior to y if x is never chosen when y is in the convex hull of the choice set. CARNI requires that an alternative is chosen if it is not inferior to all other alternatives in the convex hull of the choice set. We apply CARNI in two models and axiomatize non-binary choice correspondences. In the first model we impose the standard axioms of expected utility model, except that WARP is replaced by CARNI. We prove that it has a multiple-utility representation: There is a unique convex set of vN-M utilities, such that an alternative is chosen if and only if it is best with respect to one of the utilities in this set. In the second model we impose the axioms of the subjective expected utility, relax WARP in a similar way, and get multiple-prior representation: There is a unique convex set of priors over the state of nature, such that an alternative is chosen if and only if it is best with respect to one of these priors. Both representations are closely-related to psychological insights of justifiable choice: The decision maker has several ways to evaluate acts, each with a different justification. Observable payoff-irrelevant information during the choice triggers her to use a specific “anchoring” justification for the evaluation of the alternatives.
