Binary single-crossing random utility models

Abstract

We characterize the single-crossing random utility model (SCRUM) (Apesteguia et al. (2017)) restricted to the (experimentally and empirically) important domain of binary choice menus. As corollaries we characterize some important subclasses of SCRUM (such as single-peaked and single-dipped random utility models) on this domain. In doing so, we address instances of the (still unsolved) binary random utility problem, which asks under what conditions there is a random utility model consistent with data from binary menus.