Probability weighted means as surrogates for stochastic dominance in decision making

We discuss the role of stochastic dominance as tool for comparing uncertain payoff alternatives. However, we note the fact that this is a very strong condition and in most cases a stochastic dominance relationship does not exist between alternatives. This requires us to consider the use of surrogates for stochastic dominance to compare alternatives. Here we consider a class of surrogates that are called Probability Weighted Means (PWM). These surrogates are numeric values associated with an uncertain alternative and as such comparisons can be based on these values. The PWM are consistent with stochastic dominance in the sense that if alternative A stochastically dominated alternative B then its PWM value is larger. We look at a number of different examples of probability weighted means.