Before revision: We establish laws of large numbers for comparing sums of i.i.d. random variables in terms of stochastic dominance. Our results shed new light on a classic question, raised first by Samuelson (1963), on the relation between expected utility, risk aversion, and the aggregation of independent risks .
After revision: We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations .