Ordering risks: Expected utility theory versus Yaariʹs dual theory of risk

We introduce a class of partial orderings of risks that are dual to stochastic dominance orderings. These arise as “distortion-free” orderings in Yaariʹs dual theory of risk (1987). We show that these dual orderings are equivalent to inverse stochastic dominance orderings (Muliere and Scarsini, 1989). We motivate third dual stochastic dominance via insurance economics, while providing an alternative interpretation for second (dual) stochastic dominance. We apply dual stochastic dominance to actuarial science and show how the dual ordering of risks is related to ordering income distributions in the economics of income inequality.