Stochastic Dominance for Measure Based Uncertain Decision Making

Abstract

Our interest is in the problem of comparing alternatives with uncertain payoffs when the uncertainty is represented using a measure. We first describe various aspects of the use of a measure to represent uncertainty. We recall that probability is a special well-understood example of measure-based uncertainty. We note that stochastic dominance provides a well-established method for comparing alternatives in the case of probabilistic uncertainty. Inspired by this we develop an extension of the use of stochastic dominance for comparing uncertainty profiles to the case where the uncertainty is represented by a measure. We refer to this as measure based stochastic dominance. Do to the fact that in most cases a stochastic dominance relationship does not exist between alternatives this requires us to consider the use of surrogates for measure based stochastic dominance to compare alternatives. Here we investigate a class of surrogates for measure based stochastic dominance that we call Measure Weighted Means MWM. As we see these MWM are numeric values consistent with measure based stochastic dominance.