The concept of first-order stochastic dominance defined on distributions is inadequate in models with learning. We extend this concept to the space of distributions on distributions. We discuss conditions under which for all common observations one person's beliefs (over a set of probability...

We investigate the procedure of “random sampling” where the alternatives are random variables. When comparing any two alternatives, the decision maker samples each of the alternatives once and ranks them according to the comparison between the two realizations. Our main result is that when...