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Appraising diversity with an ordinal notion of similarity: an Axiomatic approach

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  • Sebastian Bervoets

    ()
    (IDEP-GREQAM)

  • Nicolas Gravel

    ()
    (IDEP-GREQAM)

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 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 maximax criterion.

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Bibliographic Info

Paper provided by Institut d'economie publique (IDEP), Marseille, France in its series IDEP Working Papers with number 0308.

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Length: 17 pages
Date of creation: May 2003
Date of revision:
Handle: RePEc:iep:wpidep:0308

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References

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  1. BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques.
  2. Bossert, W., 1994. "Opportunity Sets and Individual Well-Being," Working Papers 9414, University of Waterloo, Department of Economics.
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  6. Nehring,K. und C.Puppe, 1999. "A Theory of Diversity," Discussion Paper Serie A 605, University of Bonn, Germany.
  7. Nicolas Gravel & Sebastian Bervoets, 2004. "Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach," Working Papers 2004.45, Fondazione Eni Enrico Mattei.
  8. Nehring, Klaus & Puppe, Clemens, 2003. "Diversity and dissimilarity in lines and hierarchies," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 167-183, April.
  9. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  10. 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..
  11. 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.
  12. Weitzman, M.L., 1992. "Diversity Functions," Harvard Institute of Economic Research Working Papers 1610, Harvard - Institute of Economic Research.
  13. 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.
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  18. Sen, Amartya, 1988. "Freedom of choice : Concept and content," European Economic Review, Elsevier, vol. 32(2-3), pages 269-294, March.
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Cited by:
  1. Marcello Basili & Stefano Vannucci, 2007. "Diversity as Width," Department of Economics University of Siena 500, Department of Economics, University of Siena.
  2. Gaetano Gaballo & Ernesto Savaglio, 2012. "On Revealed Diversity," Department of Economics University of Siena 635, Department of Economics, University of Siena.
  3. Antoinette Baujard, 2007. "Conceptions of freedom and ranking opportunity sets. A typology," Post-Print halshs-00294466, HAL.
  4. 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.
  5. Bervoets, Sebastian & Gravel, Nicolas, 2007. "Appraising diversity with an ordinal notion of similarity: An axiomatic approach," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 259-273, May.
  6. Sebastian Bervoets, 2010. "An axiomatic approach to predictability of outcomes in an interactive setting," Theory and Decision, Springer, vol. 68(3), pages 311-323, March.
  7. S. Aulong & K. Erdlenbruch & C. Figuières, 2005. "Un tour d'horizon des critères d'évaluation de la diversité biologique," Post-Print hal-00452144, HAL.
  8. Martin Hees, 2010. "The specific value of freedom," Social Choice and Welfare, Springer, vol. 35(4), pages 687-703, October.
  9. Clemens Puppe & Yongsheng Xu, 2010. "Essential alternatives and freedom rankings," Social Choice and Welfare, Springer, vol. 35(4), pages 669-685, October.
  10. Johan Gustafsson, 2010. "Freedom of choice and expected compromise," Social Choice and Welfare, Springer, vol. 35(1), pages 65-79, June.

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