Disentangling Strict and Weak Choice in Random Expected Utility Models

We ask when a random choice rule without any axiomatic restrictions can be the result of random expected utility maximization in conjunction with a tie breaking rule. To answer this question we introduce and axiomatize the notion of a choice capacities (CCs), the (not-necessarily observable) family of sub-additive set functions representing the frequency of choice by strict maximization. The set of choice capacities is in bijection with the set of random utility models, and, critically, the set of CCs that dominate a random choice rule characterizes the set of random utility models consistent with it under some tie-breaking rule. We provide conditions on the random choice rule so as to constructively identify the consistent random utility model that produces indifference with the least frequency.