Behavioral implications of shortlisting procedures

We consider two-stage shortlisting procedures in which the menu of alternatives is first pruned by some process or criterion and then a binary relation is maximized. Given a particular first-stage process, our main result supplies a necessary and sufficient condition for choice data to be consistent with a procedure in the designated class. This result applies to any class of procedures with a certain lattice structure, including the cases of consideration filters, satisficing with salience effects, and rational shortlist methods. The theory avoids background assumptions made for mathematical convenience; in this and other respects following Richter's classical analysis of preference-maximizing choice in the absence of shortlisting.