Decision making under risk involves a ranking of distributions, which is typically based on a method for assigning a real number to a distribution using a risk measure, a premium principle or a context of expected utility. As it is typically difficult to assess a concrete risk measure or utility function it is a well established idea to use stochastic dominance rules in form of stochastic orders to compare distributions. However, it is often equally difficult to completely specify a distribution. Therefore it is an interesting question whether one can derive unambiguous decisions under partial knowledge of the distributions. In this talk we in particular address this question under the condition that we only know the mean and variance of the involved distributions or that we know the marginal distributions but not the copulas in a multivariate context. Under such assumptions we derive sufficient conditions for concepts of almost stochastic dominance that are based on restrictions on marginal utilities. The talk is based on joint work with Marco Scarsini, Ilia Tsetlin and Robert L. Winkler.