Third-degree stochastic dominance and inequality measurement

We investigate the third-degree stochastic dominance order, which is receiving increasing attention in the field of inequality measurement. Observing that this partial order fails to satisfy the von Neumann--Morgenstern independence property in the space of random variables, we introduce the concepts of strong and local third-degree stochastic dominance, which do not suffer from this deficiency. We motivate these two new binary relations and characterize them in the spirit of the Lorenz characterization of the second-degree stochastic order, comparing our findings with the closest results in inequality literature.