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Ethically Robust Comparisons of Bidimensional Distributions with an Ordinal Attribute

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  • Patrick MOYES (GREThA, CNRS, UMR 5113)
  • Nicolas GRAVEL (Aix-Marseille University and AMSE (GREQAM))

Abstract

We provide foundations for robust normative evaluation of distributions of two attributes,\r\none of which is cardinally measurable and transferable between individuals and the other is\r\nordinal and non-transferable. The result that we establish takes the form of an analogue to the standard Hardy, Littlewood, and Pólya (1934) theorem for distributions of one cardinal\r\nattribute. More specifically, we identify the transformations of the distributions which\r\nguarantee 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\r\nunanimity ranking of the distributions is equivalent to the Bourguignon (1989) ordered\r\npoverty gap quasi-ordering. Finally, we show that, if one distribution dominates another\r\naccording 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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Paper provided by Groupe de Recherche en Economie Théorique et Appliquée in its series Cahiers du GREThA with number 2011-36.

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Date of creation: 2011
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Handle: RePEc:grt:wpegrt:2011-36

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Keywords: Normative Analysis; Utilitarianism; Bidimensional Stochastic Dominance; Inequality Reducing Transformations;

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Cited by:
  1. 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).
  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. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
  4. Nicolas Gravel & Patrick Moyes, 2011. "Utilitarianism or Welfarism: Does it Make a Difference?," Working Papers halshs-00634010, HAL.
  5. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer, vol. 39(1), pages 207-251, June.
  6. Patrick MOYES (GREThA et IDEP Marseille), 2011. "Comparisons of Heterogeneous Distributions and Dominance Criteria," Cahiers du GREThA 2011-23, Groupe de Recherche en Economie Théorique et Appliquée.
  7. Patrick MOYES, 2013. "Rearrangements and Sequential Rank Order Dominance," Cahiers du GREThA 2013-10, Groupe de Recherche en Economie Théorique et Appliquée.
  8. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
  9. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART.
  10. Muller, Christophe & Trannoy, Alain, 2012. "Multidimensional inequality comparisons: A compensation perspective," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1427-1449.

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