Preference Structures. II: Distances Between Asymmetric Relations

Abstract

In this paper the results of Preference structures I are extended to not necessarily transitive relations. The extension of the city block metric of [3] leads to a discussion of the relation of majority rule to the median of a collection of relations. The extension of the Euclidean metric of [3] leads to a discussion of the mean of a collection of relations and methods for finding means. Finally, the extension of the Euclidean metric leads to a discussion of statistical inference about random variables whose ranges are preference relations.