Appraising diversity with an ordinal notion of similarity: An axiomatic approach

This paper axiomatically characterizes a rule 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 quaternary relation that compares alternative pairs of objects on the basis of their dissimilarity. The rule that we characterize is the maxi-max criterion. It considers that a set is more diverse than another if and only if the two most dissimilar objects in the former are weakly as dissimilar as the two most dissimilar objects in the later. Some connections with the issue of appraising freedom of choice are also provided.