Choice Functions Generated by Mallows and Plackett–Luce Relations

Abstract

The rationality and consistency of preference-based choice functions is often studied for (fuzzy) preference relations having specific properties, such as strong completeness, transitivity, or certain properties on triplets. In this paper, we turn our attention to another type of preference relation, namely relations that are induced as pairwise marginal of an underlying probability distribution on complete rankings (permutations) of all given alternatives. Such relations are necessarily reciprocal and, depending on the underlying distribution, obey additional structural properties. More specifically, we study relations induced by two important probability distributions, the Mallows and the Plackett–Luce distribution, which are well-known in the literature on statistics of rank data. Assuming preference relations of this kind, we study seven different choice functions and their four rationality and consistency properties.