Stochastic dominance in multi sampling environments

Stochastic dominance rules are constructed for environments in which individuals sample sequentially according to a stopping rule. The dominance criterion used requires that all sampling take place in the dominant distribution with probability one even if the individual is permitted to switch during the course of sampling. The principal resultis that the necessary dominance criterion is (conventional) first degree stochastic dominance even if individuals are "very" risk averse. On the other hand, knowledge of an upper bound on risk aversion ranks random variables identically in both sampling and nonsampling environments.