Professor of Decision Sciences
Downside Risk; Precautionary Effects; Prudence; Risk Apportionment; Risk Aversion; Stochastic Dominance; Temperance; IAF 08/09; IAF 2520064;
Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via i th-order stochastic dominance for i = M,N. We show that the 50–50 lottery [XN + YM,YN + XM] dominates the lottery [XN + XM,YN + YM] via (N + M) th-order stochastic dominance.The basic idea is that a decision maker exhibiting (N + M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two “bad” lotteries in the same state, where “bad” is defined via ith-order stochastic dominance.In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher-order risk effects, such as recautionary effects and tempering effects.