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

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Listed:
  • Nicolas Gravel

    (IDEP-GREQAM and Université de la Méditerranée)

  • Sebastian Bervoets

    (IDEP-GREQAM and Université de la Méditerranée)

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.

Suggested Citation

  • Nicolas Gravel & Sebastian Bervoets, 2004. "Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach," Working Papers 2004.45, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2004.45
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    References listed on IDEAS

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    Cited by:

    1. Yang Shen & Jing Wu & Shuping Wu, 2022. "City‐chief turnover and place‐based policy change: Evidence from China," Journal of Regional Science, Wiley Blackwell, vol. 62(5), pages 1296-1328, November.
    2. Stéphanie Aulong & Katrin Erdlenbruch & C. Figuières, 2005. "Un tour d'horizon des critères d'évaluation de la diversité biologique," Post-Print hal-00452144, HAL.
    3. 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.
    4. 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.
    5. Gaetano Gaballo & Ernesto Savaglio, 2012. "On revealed diversity," Working Papers 254, ECINEQ, Society for the Study of Economic Inequality.
    6. 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.
    7. 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.
    8. 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.
    9. Richter, Marcel K. & Wong, Kam-Chau, 2016. "Likelihood relations and stochastic preferences," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 28-35.
    10. 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.
    11. Gaetano Gaballo & Ernesto Savaglio, 2012. "On Revealed Diversity," Department of Economics University of Siena 635, Department of Economics, University of Siena.
    12. Antoinette Baujard, 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.
    13. 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.
    14. 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.
    15. 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.

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    More about this item

    Keywords

    Diversity; Measurement; Axioms; Freedom of choice;
    All these keywords.

    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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