Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable (X) over tilde (i) dominates (Y) over tilde (i) via ith-order stochastic dominance for i = M, N. We show that the 50-50 lottery [(X) over tilde (N) + (Y) over tilde (M), (Y) over tilde (N) + (X) over tilde (M)] dominates the lottery [(X) over tilde (N) + (X) over tilde (M), (Y) over tilde (N) + (Y) over tilde (M) 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 precautionary effects and tempering effects.