Graded Stochastic Dominance as a Tool for Ranking the Elements of a Poset

摘要

Three methods are outlined aiming at the (partial) ranking of the elements of a poset respecting the poset order. First, we obtain a partial ranking by applying first degree stochastic dominance to the rank probability distributions of the poset elements. Then we use the minimum, product or Lukasiewicz copula as an artefact for pairwisely coupling rank probability distributions into bivariate distributions. They serve as a basis for generating a probabilistic relation which constitutes a graded version of stochastic dominance. The transitivity of the probabilistic relations being characterizable in the framework of cycle-transitivity, a cutting level is specified that provides us with a strict partial order. Finally, we apply the graded stochastic dominance principle directly to the mutual rank probabilities. Based on exhaustive experiments, a conjecture on the transitivity of the associated probabilistic relation is made, and a (partial) ranking of the poset elements is extracted.