Multivariate winning probabilities

Abstract Stochastic dominance and statistical preference are two important tools for the pairwise comparison of random variables. However, pairwise methods are not always appropriate in the case of more than two alternatives. In this work, we generalize the notion of winning probability to the notion of multivariate winning probability. The latter allows to establish a ranking (with ties) on any set of random variables and naturally leads to the notion of probabilistic preference. We investigate the relationship between the latter notion and the classical notions of stochastic dominance and statistical preference.

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