We consider an agent who chooses from a set of options after receiving some private information. This information however is unobserved by an analyst, so from the latter’s perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random choice. In ad-dition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex-ante valuations of option sets from ran-dom choice and vice-versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent’s beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well-calibrated or rational. ⇤ I am deeply indebted to both Faruk Gul and Wolfgang Pesendorfer for their continuous advice, guidance and encouragement. I am very grateful to Stephen Morris for some highly valuable and insightful discussions.

We propose a novel model of stochastic choice: the single-crossing random utility model (SCRUM). This is a random utility model in which the collection of preferences satisfies the single-crossing property. We o↵er a characterization of SCRUMs based on two easy-to-check properties: the classic Monotonicity property and a novel condition, Centrality. The identified collection of preferences and associated probabilities is unique. We show that SCRUMs nest both single-peaked and single-dipped random utility models and establish a stochastic monotone comparative result for the case of SCRUMs.