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Ethically robust comparisons of bidimensional distributions with an ordinal attribute

  • Gravel, Nicolas
  • Moyes, Patrick

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Margaret Meyer & Bruno Strulovici, 2011. "Increasing Interdependence of Multivariate Distributions," Discussion Papers 1523, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
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  5. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  8. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
  9. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931, March.
  10. Beach, Charles M & Davidson, Russell, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 723-35, October.
  11. Patrick MOYES (GREThA, CNRS, UMR 5113), 2011. "Rearrangements and Sequential Rank Order Dominance. A Result with Economic Applications," Cahiers du GREThA 2011-35, Groupe de Recherche en Economie Théorique et Appliquée.
  12. 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.
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  14. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March.
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  16. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  17. Nicolas Gravel & Patrick Moyes, 2011. "Utilitarianism or Welfarism: Does it Make a Difference?," Working Papers halshs-00634010, HAL.
  18. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
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  20. Peter C. Fishburn, 1978. "Stochastic Dominance Without Transitive Preferences," Management Science, INFORMS, vol. 24(12), pages 1268-1277, August.
  21. Fleurbaey, Marc & Hagnere, Cyrille & Trannoy, Alain, 2003. "Welfare comparisons with bounded equivalence scales," Journal of Economic Theory, Elsevier, vol. 110(2), pages 309-336, June.
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  23. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
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  28. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
  29. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
  30. Bishop, John A & Chakraborti, S & Thistle, Paul D, 1989. "Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves," The Review of Economics and Statistics, MIT Press, vol. 71(4), pages 725-27, November.
  31. Nicolas Gravel & Patrick Moyes & Beno�T Tarroux, 2009. "Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods," Economica, London School of Economics and Political Science, vol. 76(303), pages 432-461, 07.
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