A hyper-relation characterization of weak pseudo-rationalizability

I provide a characterization of weakly pseudo-rationalizable choice functions – that is, choice functions rationalizable by a set of acyclic relations – in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.