Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications

We characterize the extreme points of first-order stochastic dominance (FOSD) intervals and show how these intervals are at the heart of many topics in economics. Using knowledge of these extreme points, we characterize the distributions of posterior quantiles under a given prior, leading to an analogue of a classical result regarding the distribution of posterior means. We apply this analogue to various economic subjects, including the psychology of judgement, political economy, and Bayesian persuasion. In addition, FOSD intervals provide a common structure to security design. We use the extreme points to unify and generalize seminal results in that literature when either adverse selection or moral hazard pertains.