Dominance and optimality

We introduce a theory of dominance that encompasses as special cases the theory of admissible decision procedures in statistics, strict and weak dominance among strategies in games, first or second-order stochastic dominance among monetary lotteries, and Pareto dominance among social alternatives. One choice dominates another if in a variety of situations the former choice yields higher expected utility than the latter. We show that under certain assumptions, which include most importantly convexity of the set of situations, and linearity of the decision maker’s utility function in the argument that describes the situation, all undominated choices are optimal in some situation. We show this result for three different definitions of dominance. Our analysis of existing dominance notions in economics in one common framework allows us to compare the properties of these concepts, and to obtain insights into why certain versions of our result apply only to some, but not all of these concepts. We motivate the concept of undominated strategies by developing a formal result relating undominated strategies to rational inattention. As an application that illustrates the general theory we investigate Blackwell dominance among experiments.