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Ethically Robust Comparisons of Distributions of Two Individual Attributes

This paper examines the normative properties of an empirically implementable dominance criterion for comparing alternative distributions of two attributes, one of which being cardinally measurable, between an arbitrary number of individuals. The criterion, which generalizes the one proposed by Bourguignon (1989), states that distribution A dominates distribution B when poverty in the cardinally measurable attribute, as measured by the poverty gap, is no greater in A than in B for all poverty lines that are weakly decreasing with respect to the other attribute. The criterion is shown to be equivalent to the ranking of distributions of two attributes that would be aggreed upon by all utility-inequality averse welfarist social planners who assume that households convert attributes into well-being by the same increasing utility function satisfying the property that the marginal utility of the cardinally measurable attribute is decreasing with respect to the two attributes. This paper also identifies the elementary equalizing transformations that correspond to this criterion.

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Paper provided by Institut d'economie publique (IDEP), Marseille, France in its series IDEP Working Papers with number 0605.

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Length: 51 pages
Date of creation: Aug 2006
Date of revision: Aug 2006
Handle: RePEc:iep:wpidep:0605
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  1. 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.
  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.
  3. 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.
  4. 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.
  5. d'ASPREMONT, Claude & GEVERS, Louis, . "Equity and the informational basis of collective choice," CORE Discussion Papers RP -350, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Vincenzo DenicolÔ, 1999. "A characterization of utilitarianism without the transitivity axiom," Social Choice and Welfare, Springer, vol. 16(2), pages 273-278.
  7. Beach, Charles M. & Chow, K. Victor & Formby, John P. & Slotsve, George A., 1994. "Statistical inference for decile means," Economics Letters, Elsevier, vol. 45(2), pages 161-167, June.
  8. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Vanderbilt University Department of Economics Working Papers 0314, Vanderbilt University Department of Economics, revised Jan 2004.
  9. Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
  10. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  11. Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer, vol. 15(1), pages 1-14.
  12. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
  13. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
  14. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
  15. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  16. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
  17. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
  18. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
  19. Ian Crawford, 2005. "A nonparametric test of stochastic dominance in multivariate distributions," School of Economics Discussion Papers 1205, School of Economics, University of Surrey.
  20. Kaur, Amarjot & Prakasa Rao, B.L.S. & Singh, Harshinder, 1994. "Testing for Second-Order Stochastic Dominance of Two Distributions," Econometric Theory, Cambridge University Press, vol. 10(05), pages 849-866, December.
  21. 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.
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