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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.

Suggested Citation

  • Sebastian Bervoets & Nicolas Gravel, 2003. "Appraising diversity with an ordinal notion of similarity: an Axiomatic approach," IDEP Working Papers 0308, Institut d'economie publique (IDEP), Marseille, France.
    • Handle: RePEc:iep:wpidep:0308
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    1. Pattanaik, Prasanta K. & Xu, Yongsheng, 2000. "On diversity and freedom of choice," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 123-130, September.
    2. Sugden, Robert, 1985. "Liberty, Preference, and Choice," Economics and Philosophy, Cambridge University Press, vol. 1(2), pages 213-229, October.
    3. Walter Bossert, 1996. "Opportunity sets and individual well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 97-112.
    4. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
    5. Martin L. Weitzman, 1998. "The Noah's Ark Problem," Econometrica, Econometric Society, vol. 66(6), pages 1279-1298, November.
    6. Martin L. Weitzman, 1992. "On Diversity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 363-405.
    7. Klaus Nehring, "undated". "A Theory Of Qualitative Similarity," Department of Economics 97-10, California Davis - Department of Economics.
    8. N. Gravel & J.-F. Laslier & A. Trannoy, 1996. "Individual freedom of choice in a social setting," THEMA Working Papers 96-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    9. Walter Bossert & Prasanta K. Pattanaik & Yongsheng Xu, 2003. "Similarity of Options and the Measurement of Diversity," Journal of Theoretical Politics, , vol. 15(4), pages 405-421, October.
    10. Antonio Romero-Medina, 2001. "More on preference and freedom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 179-191.
    11. Patrick Suppes, 1996. "The nature and measurement of freedom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 183-200, April.
    12. Martin L. Weitzman, 1993. "What to Preserve? An Application of Diversity Theory to Crane Conservation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 157-183.
    13. 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.
    14. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    15. 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.
    16. Prasanta K. PATTANAIK & Yongsheng XU, 1990. "On Ranking Opportunity Sets in Terms of Freedom of Choice," Discussion Papers (REL - Recherches Economiques de Louvain) 1990036, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    17. Nehring, Klaus & Puppe, Clemens, 2003. "Diversity and dissimilarity in lines and hierarchies," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 167-183, April.
    18. 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.
    19. Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
    20. Sen, Amartya, 1988. "Freedom of choice : Concept and content," European Economic Review, Elsevier, vol. 32(2-3), pages 269-294, March.
    21. Weitzman, M.L., 1992. "Diversity Functions," Harvard Institute of Economic Research Working Papers 1610, Harvard - Institute of Economic Research.
    22. Basu, K. & Pattanaik, P. K. & Suzumura, K. (ed.), 1995. "Choice, Welfare, and Development: A Festschrift for Amartya K. Sen," OUP Catalogue, Oxford University Press, number 9780198287896.
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    Cited by:

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    2. Clemens Puppe & Yongsheng Xu, 2010. "Essential alternatives and freedom rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 669-685, October.
    3. Stéphanie Aulong & Katrin Erdlenbruch & C. Figuières, 2005. "Un tour d'horizon des critères d'évaluation de la diversité biologique," Post-Print hal-00452144, HAL.
    4. Gaetano Gaballo & Ernesto Savaglio, 2012. "On Revealed Diversity," Department of Economics University of Siena 635, Department of Economics, University of Siena.
    5. Antoinette Baujard, 2006. "Conceptions of freedom and ranking opportunity sets. A typology," Economics Working Paper Archive (University of Rennes & University of Caen) 200611, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    6. Martin Hees, 2010. "The specific value of freedom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 687-703, October.
    7. Johan Gustafsson, 2010. "Freedom of choice and expected compromise," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 65-79, June.
    8. 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.
    9. Gaetano Gaballo & Ernesto Savaglio, 2012. "On revealed diversity," Working Papers 254, ECINEQ, Society for the Study of Economic Inequality.
    10. Ronen Shnayderman, 2016. "Ian Carter’s non-evaluative theory of freedom and diversity: a critique," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 39-55, January.
    11. 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.
    12. 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.
    13. Elżbieta Pliś, 2020. "Diversity and Innovation in Economic Evolution," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(4), pages 347-367, December.
    14. Marcello Basili & Stefano Vannucci, 2013. "Diversity as width," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 913-936, March.
    15. Richter, Marcel K. & Wong, Kam-Chau, 2016. "Likelihood relations and stochastic preferences," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 28-35.

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    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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