Abstract
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.