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

Nicolas Gravel () and Sebastian Bervoets

No 2004.45, Working Papers from Fondazione Eni Enrico Mattei

Abstract: 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.

Keywords: Diversity; Measurement; Axioms; Freedom of choice (search for similar items in EconPapers)
JEL-codes: D63 D69 Q20 (search for similar items in EconPapers)
Date: 2004-03
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Appraising diversity with an ordinal notion of similarity: An axiomatic approach (2007)
Working Paper: Appraising diversity with an ordinal notion of similarity: an Axiomatic approach (2003)
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