Increasing Discriminatory Power in Well-being Analysis using Convex Stochastic Dominance

The complementary concepts of Stochastic Dominance Optimality and Stochastic Dominance Inferiority are developed and employed to detect collections of distributions with the highest and lowest levels of shared prosperity respectively. These resulting sets can be smaller than the standard sets of maximal and minimal elements based on multiple pairwise comparisons. Linear Programming techniques for implementing the twin concepts are derived and implemented in empirical and simulated examples based on aggregated income distributions to demonstrate the potential gains in discriminatory power.