Before revision: Ranking gambles by mean-preserving spreads is a special case of ranking gambles by second-order stochastic dominance – namely, the special case of equal means: If B is a mean-preserving spread of A, then A is second-order stochastically dominant over B ; and the converse holds if A and B have equal means.
After revision: Ranking gambles by mean-preserving spreads is a special case of ranking gambles by second-order stochastic dominance – namely, the special case of equal means: If B is a mean-preserving spread of B, then A is second-order stochastically dominant over A ; and the converse holds if A and B have equal means.