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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

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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 40 (2013)
Issue (Month): 3 (March)
Pages: 913-936

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Handle: RePEc:spr:sochwe:v:40:y:2013:i:3:p:913-936

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  1. Prasanta Pattanaik & Yongsheng Xu, 1998. "On Preference and Freedom," Theory and Decision, Springer, vol. 44(2), pages 173-198, April.
  2. Pattanaik, Prasanta K. & Xu, Yongsheng, 2000. "On diversity and freedom of choice," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 123-130, September.
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  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. BOSSERT, Walter & PATTANAIK, Prasanta K. & XU, Yongsheng, 2001. "The Measurement of Diversity," Cahiers de recherche 2001-17, Universite de Montreal, Departement de sciences economiques.
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  7. Weitzman, Martin L, 1992. "On Diversity," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 363-405, May.
  8. Martin L. Weitzman, 1998. "The Noah's Ark Problem," Econometrica, Econometric Society, vol. 66(6), pages 1279-1298, November.
  9. BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques.
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  11. Stefano Vannucci, 2006. "On Concept Lattices of Efficiently Solvable Voting Protocols," Department of Economics University of Siena 489, Department of Economics, University of Siena.
  12. 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.
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Cited by:
  1. Gaetano Gaballo & Ernesto Savaglio, 2012. "On revealed diversity," Working Papers 254, ECINEQ, Society for the Study of Economic Inequality.
  2. Stefano Vannucci, 2011. "Widwast Choice," Department of Economics University of Siena 629, Department of Economics, University of Siena.

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