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Comparisons of Heterogeneous Distributions and Dominance Criteria

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  • Patrick MOYES

Abstract

We are interested in the comparisons of standard-of-living across societies when observations of both income and household structure are available. We generalise the approach of Atkinson and Bourguignon (1987) to the case where the marginal distributions of needs can vary across the household populations under comparison. We assume that a sympathetic observer uses a utilitarian social welfare function in order to rank heterogeneous income distributions. Insofar as any individual can play the role of the observer, we take the unanimity point of view according to which the planner’s judgements have to comply with a certain number of basic normative principles. We impose increasingly restrictive conditions on the household’s utility function and we investigate their effects on the resulting rankings of the distributions. This leads us to propose four dominance criteria that can be used for providing an unambiguous ranking of income distributions for heterogeneous populations.

Suggested Citation

  • Patrick MOYES, 2011. "Comparisons of Heterogeneous Distributions and Dominance Criteria," Cahiers du GREThA (2007-2019) 2011-23, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
  • Handle: RePEc:grt:wpegrt:2011-23
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    Cited by:

    1. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
    2. 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.
    3. Marling, Tina Gottschalk & Range, Troels Martin & Sudhölter, Peter & Østerdal, Lars Peter, 2018. "Decomposing bivariate dominance for social welfare comparisons," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 1-8.
    4. Marc Fleurbaey & Cyrille Hagneré & Alain Trannoy, 2007. "Welfare Comparisons of Income Distributions and Family Size," IDEP Working Papers 0702, Institut d'economie publique (IDEP), Marseille, France, revised 16 Jan 2007.
    5. Benoît Tarroux, 2015. "Comparing two-dimensional distributions: a questionnaire-experimental approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 87-108, January.
    6. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    7. Christophe Muller, 2019. "Social Shock Sharing and Stochastic Dominance," AMSE Working Papers 1903, Aix-Marseille School of Economics, France.
    8. Peter J. Lambert & Xavier Ramos, 2001. "Welfare comparisons: sequential procedures for heterogenous population," Working Papers wp0114, Department of Applied Economics at Universitat Autonoma of Barcelona.
    9. Muller, Christophe & Trannoy, Alain, 2011. "A dominance approach to the appraisal of the distribution of well-being across countries," Journal of Public Economics, Elsevier, vol. 95(3-4), pages 239-246, April.
    10. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.
    11. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    12. Mathieu Faure & Nicolas Gravel, 2021. "Reducing Inequalities Among Unequals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(1), pages 357-404, February.
    13. Christophe Muller & Alain Trannoy, 2003. "A Dominance Approach to Well-Being Inequality across Countries," IDEP Working Papers 0313, Institut d'economie publique (IDEP), Marseille, France.
    14. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2019. "Inequality measurement with an ordinal and continuous variable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 453-475, March.
    15. N. GRAVEL & Patrick MOYES, 2008. "Bidimensional Inequalities with an Ordinal Variable," Cahiers du GREThA (2007-2019) 2008-14, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    16. Patrick MOYES, 2011. "Rearrangements and Sequential Rank Order Dominance. A Result with Economic Applications," Cahiers du GREThA (2007-2019) 2011-35, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    17. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series wp-2013-097, World Institute for Development Economic Research (UNU-WIDER).
    18. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    19. Dubois, Marc & Mussard, Stéphane, 2019. "Utility and income transfer principles: Interplay and incompatibility," Mathematical Social Sciences, Elsevier, vol. 100(C), pages 46-56.
    20. Sonne-Schmidt, Christoffer & Tarp, Finn & Østerdal, Lars Peter, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series 097, World Institute for Development Economic Research (UNU-WIDER).
    21. Nicolas Gravel & Patrick Moyes, 2011. "Bidimensional Inequalities with an Ordinal Variable," Studies in Choice and Welfare, in: Marc Fleurbaey & Maurice Salles & John A. Weymark (ed.), Social Ethics and Normative Economics, pages 101-127, Springer.
    22. Mathews, Timothy & Schwartz, Jesse A., 2019. "Comparisons of utility inequality and income inequality," Economics Letters, Elsevier, vol. 178(C), pages 18-20.
    23. Udo Ebert & Patrick Moyes, 2017. "Inequality and isoelastic equivalence scales: restrictions and implications," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 295-326, February.

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    More about this item

    Keywords

    Normative Analysis; Utilitarianism; Welfarism; Multidimensional Inequality and Welfare; Bidimensional Stochastic Dominance; Inequality Reducing Transformations.;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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