A Correspondence Between Methods for Ranking Elements of a Poset and Stochastic Orderings

Stochastic orderings are a commonly used tool in probability theory for comparing random variables or probability distributions. In a recent publication we showed that stochastic orderings are, to some extent, in correspondence with voting procedures. For instance, we demonstrated that the Borda count is equivalent to the comparison of expectations while the Condorcet method is equivalent to statistical preference. This contribution establishes as well a correspondence between stochastic orderings and methods used in the literature for ranking the elements of a poset. Specifically, we show that some well-known methods used in the literature for ranking the elements of a poset, namely the averaged ranking, mutual rank probabilities and the maximal method, are formally equivalent to comparing expectations, statistical preference and multivariate probabilistic preference, respectively.