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

  • Nicolas Gravel

    (IDEP-GREQAM and Université de la Méditerranée)

  • Sebastian Bervoets

    (IDEP-GREQAM and Université de la Méditerranée)

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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  1. Bossert, W., 1994. "Opportunity Sets and Individual Well-Being," Working Papers 9414, University of Waterloo, Department of Economics.
  2. Martin L. Weitzman, 1998. "The Noah's Ark Problem," Econometrica, Econometric Society, vol. 66(6), pages 1279-1298, November.
  3. Nehring,K. und C.Puppe, 1999. "A Theory of Diversity," Discussion Paper Serie A 605, University of Bonn, Germany.
  4. Weitzman, Martin L, 1993. "What to Preserve? An Application of Diversity Theory to Crane Conservation?," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 157-83, February.
  5. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
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  8. Patrick Suppes, 1996. "The nature and measurement of freedom," Social Choice and Welfare, Springer, vol. 13(2), pages 183-200, April.
  9. Nehring, Klaus & Puppe, Clemens, 2003. "Diversity and dissimilarity in lines and hierarchies," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 167-183, April.
  10. Weitzman, Martin L, 1992. "On Diversity," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 363-405, May.
  11. Nicolas Gravel & Sebastian Bervoets, 2004. "Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach," Working Papers 2004.45, Fondazione Eni Enrico Mattei.
  12. Antonio Romero-Medina, 2001. "More on preference and freedom," Social Choice and Welfare, Springer, vol. 18(1), pages 179-191.
  13. BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques.
  14. Sen, Amartya, 1988. "Freedom of choice : Concept and content," European Economic Review, Elsevier, vol. 32(2-3), pages 269-294, March.
  15. Sugden, Robert, 1985. "Liberty, Preference, and Choice," Economics and Philosophy, Cambridge University Press, vol. 1(02), pages 213-229, October.
  16. Weitzman, M.L., 1992. "Diversity Functions," Harvard Institute of Economic Research Working Papers 1610, Harvard - Institute of Economic Research.
  17. 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.
  18. Gravel, N. & Laslier, J.F. & Trannoy, A., 1996. "Individual Freedom of Choice in a Social Setting," Papers 9625, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
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