Invariance of the efficient sets when the expected utility hypothesis is relaxed

We consider risk averse decision makers who choose from a given set X of random variables and whose preference ordering need not be transitive or representable by a real utility index. We show that when all nonlinear preference functionals possess the first and the second degree stochastic dominance, the efficient set in X remains unchanged. We apply this result to Arrow's (1974) theory about the structure of optimal insurance contracts.