Weak pseudo-rationalizability

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This result also generalizes Aizerman and Malishevski’s characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. •I characterize rationalizability by a set of acyclic binary relations.•The relevant properties are Sen’s property α and a weakening of Sen’s property γ.•This result generalizes the decomposition for pseudo-rationalizable choice functions.