Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach

This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a finite universe of objects and an a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. Very few properties of this quadernary relation are assumed (beside completeness, transitivity and a very natural form of symmetry). The two rules that we characterize are the maxi-max criterion and the lexi-max criterion. The maxi-max criterion considers that a set is more diverse than another if and only if the two objects that are the most dissimilar in the former are weakly as dissimilar as the two most dissimilar objects in the later. The lexi-max criterion is defined as usual as the lexicographic extension of the maxi-max criterion. Some connections with the broader issue of measuring freedom of choice are also provided.Diversity, Measurement, Axioms, Freedom of choice

On Preference, Freedom and Diversity

We study the problem of ranking sets of options in terms of freedom of choice. We propose a framework in which both the diversity of the options and the preferences of the agent over the options do play a role. We formulate some axioms that reflect these two aspects of freedom and we study their logical implications. Two diifferent criteria for ranking sets are characterized, which generalize some of the rankings proposed so far in the literatureRanking Sets; Freedom of Choice; Diversity relations