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Ethically robust comparisons of bidimensional distributions with an ordinal attribute

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  • Gravel, Nicolas
  • Moyes, Patrick

Abstract

We provide foundations for robust normative evaluation of distributions of two attributes, one of which is cardinally measurable and transferable between individuals and the other is ordinal and non-transferable. The result that we establish takes the form of an analogue to the standard Hardy–Littlewood–Pólya theorem for distributions of one cardinal attribute. More specifically, we identify the transformations of the distributions which guarantee that social welfare increases according to utilitarian unanimity provided that the utility function is concave in the cardinal attribute and that its marginal utility with respect to the same attribute is non-increasing in the ordinal attribute. We establish that this unanimity ranking of the distributions is equivalent to the ordered poverty gap quasi-ordering introduced by Bourguignon [12]. Finally, we show that, if one distribution dominates another according to the ordered poverty gap criterion, then the former can be derived from the latter by means of an appropriate and finite sequence of such transformations.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 4 ()
Pages: 1384-1426

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1384-1426

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Normative analysis; Utilitarianism; Bidimensional stochastic dominance; Inequality reducing transformations;

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References

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Citations

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Cited by:
  1. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
  2. Range, Troels Martin & Østerdal, Lars Peter, 2013. "Checking bivariate first order dominance," Discussion Papers of Business and Economics 9/2013, Department of Business and Economics, University of Southern Denmark.
  3. Nicolas Gravel & Patrick Moyes, 2011. "Utilitarianism or Welfarism: Does it Make a Difference?," Working Papers halshs-00634010, HAL.
  4. Moyes, Patrick, 2012. "Comparisons of heterogeneous distributions and dominance criteria," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1351-1383.
  5. Patrick MOYES, 2013. "Rearrangements and Sequential Rank Order Dominance," Cahiers du GREThA 2013-10, Groupe de Recherche en Economie Théorique et Appliquée.
  6. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
  7. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
  8. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer, vol. 39(1), pages 207-251, June.
  9. Muller, Christophe & Trannoy, Alain, 2012. "Multidimensional inequality comparisons: A compensation perspective," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1427-1449.
  10. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART.
  11. Sonne-Schmidt, Christoffer & Tarp, Finn & Osterdal, Lars Peter, 2013. "Ordinal multidimensional inequality," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).

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