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Diversity as width

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  • Marcello Basili
  • Stefano Vannucci

Abstract

It is argued that if a finite partially ordered population is given, and incomparability is taken as the relevant type of dissimilarity, then diversity comparisons between subpopulations may be conveniently based on widths namely on the maximum number of pairwise incomparable units they include. We introduce two width-based rankings. The first one is the plain width-ranking of subposets as induced by width computation. The second one is the undominated width-ranking of subposets namely the ranking induced by the sizes of undominated subposets. Simple axiomatic characterizations of the foregoing rankings are provided. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:40:y:2013:i:3:p:913-936
    DOI: 10.1007/s00355-011-0649-8
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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. Martin L. Weitzman, 1998. "The Noah's Ark Problem," Econometrica, Econometric Society, vol. 66(6), pages 1279-1298, November.
    3. Martin L. Weitzman, 1992. "On Diversity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 363-405.
    4. 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.
    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. Grabisch, Michel, 2006. "Representation of preferences over a finite scale by a mean operator," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 131-151, September.
    7. BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques.
    8. Martin van Hees, 2004. "Freedom of choice and diversity of options: Some difficulties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(1), pages 253-266, February.
    9. Vito Peragine & Antonio Romero-Medina, 2006. "On Preference, Freedom and Diversity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 29-40, August.
    10. Stefano Vannucci, 2006. "On Concept Lattices of Efficiently Solvable Voting Protocols," Department of Economics University of Siena 489, Department of Economics, University of Siena.
    11. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
    12. BOSSERT, Walter & PATTANAIK, Prasanta K. & XU, Yongsheng, 2001. "The Measurement of Diversity," Cahiers de recherche 2001-17, Universite de Montreal, Departement de sciences economiques.
    13. Prasanta Pattanaik & Yongsheng Xu, 1998. "On Preference and Freedom," Theory and Decision, Springer, vol. 44(2), pages 173-198, April.
    14. Nehring, Klaus & Puppe, Clemens, 2003. "Diversity and dissimilarity in lines and hierarchies," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 167-183, April.
    15. Weitzman, M.L., 1992. "Diversity Functions," Harvard Institute of Economic Research Working Papers 1610, Harvard - Institute of Economic Research.
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    Cited by:

    1. Mauro Caminati, 2021. "Knowledge distance and R&D collaboration in Cournot oligopoly," Metroeconomica, Wiley Blackwell, vol. 72(1), pages 57-81, February.
    2. Gaetano Gaballo & Ernesto Savaglio, 2012. "On revealed diversity," Working Papers 254, ECINEQ, Society for the Study of Economic Inequality.
    3. Gaetano Gaballo & Ernesto Savaglio, 2012. "On Revealed Diversity," Department of Economics University of Siena 635, Department of Economics, University of Siena.
    4. Stefano Vannucci, 2011. "Widwast Choice," Department of Economics University of Siena 629, Department of Economics, University of Siena.

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    JEL classification:

    • D00 - Microeconomics - - General - - - General
    • Q00 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - General
    • Z00 - Other Special Topics - - General - - - General

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