Third Degree Stochastic Dominance and the von Neumann-Morgenstern Independence Property

This paper is an investigation of the third-degree stochastic dominance order which has been introduced in the context of risk analysis and is now receiving an increased attention in the area of inequality measurement. After observing that this partial order fails to satisfy the von Neumann-Morgenstern property in the space of random variables, we introduce strong and local third-degree stochastic dominance. We motivate these two new binary relations and offer a complete and simple characterizations in the spirit of the Lorenz characterization of the second-degree stochastic order. The paper compares our results with the closest literature. JEL Classification Numbers: D31, D63.