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

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Author Info
Nicolas Gravel (IDEP-GREQAM and Université de la Méditerranée)
Sebastian Bervoets (IDEP-GREQAM and Université de la Méditerranée)

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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.

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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.45.

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Date of creation: Mar 2004
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Handle: RePEc:fem:femwpa:2004.45

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Related research
Keywords: Diversity; Measurement; Axioms; Freedom of choice;

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Find related papers by JEL classification:
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
D69 - Microeconomics - - Welfare Economics - - - Other
Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Walter Bossert, 1996. "Opportunity sets and individual well-being," Social Choice and Welfare, Springer, vol. 14(1), pages 97-112. [Downloadable!] (restricted)
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  2. Weitzman, Martin L, 1992. "On Diversity," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 363-405, May. [Downloadable!] (restricted)
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  3. Dutta, Bhaskar & Sen, Arunava, 1996. "Ranking Opportunity Sets and Arrow Impossibility Theorems: Correspondence Results," Journal of Economic Theory, Elsevier, vol. 71(1), pages 90-101, October. [Downloadable!] (restricted)
  4. Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June. [Downloadable!] (restricted)
  5. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May. [Downloadable!] (restricted)
  6. Sen, Amartya, 1988. "Freedom of choice : Concept and content," European Economic Review, Elsevier, vol. 32(2-3), pages 269-294, March. [Downloadable!] (restricted)
  7. Antonio Romero-Medina, 2001. "More on preference and freedom," Social Choice and Welfare, Springer, vol. 18(1), pages 179-191. [Downloadable!] (restricted)
  8. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  1. Ricardo Arlegi, 2005. "Freedom Of Choice And Conflict Resolution," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0502, Departamento de Economía - Universidad Pública de Navarra. [Downloadable!]
  2. Antoinette Baujard (CREM - CNRS), 2006. "Conceptions of freedom and ranking opportunity sets. A typology," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200611, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS. [Downloadable!]
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