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Bidimensional inequalities with an ordinal variable

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  • Patrick Moyes

    (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

Abstract

We investigate the normative foundations of two empirically implementable dominance criteria for comparing distributions of two attributes, where the first one is cardinal while the second is ordinal. The criteria we consider are Atkinson and Bourguignon\'s (1982) first quasi-ordering and a generalization of Bourguignon\'s (1989) ordered poverty gap criterion. In each case we specify the restrictions to be placed on the individual utility functions, which guarantee that all utility-inequality averse welfarist ethical observers will rank the distributions under comparison in the same way as the dominance criterion. We also identify the elementary inequality reducing transformations successive applications of which permit to derive the dominating distribution from the dominated one.
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Suggested Citation

  • Patrick Moyes, 2009. "Bidimensional inequalities with an ordinal variable," Post-Print hal-00285476, HAL.
    • Handle: RePEc:hal:journl:hal-00285476
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    References listed on IDEAS

    as
    1. 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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    5. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-1135, September.
    6. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
    7. Moyes, Patrick, 2012. "Comparisons of heterogeneous distributions and dominance criteria," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1351-1383.
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    12. Stephen Bazen & Patrick Moyes, 2003. "International comparisons of income distributions when population structures differ," Post-Print hal-00156458, HAL.
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    21. N. Gravel & Patrick Moyes & B. Tarroux, 2008. "Robust international comparisons of distributions of disposable income and access to regional public goods," Post-Print hal-00157357, HAL.
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    25. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
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    Cited by:

    1. Nicolas Gravel & Patrick Moyes, 2013. "Utilitarianism or welfarism: does it make a difference?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 529-551, February.
    2. C. Schluter & D. Van De Gaer, 2008. "Structural Mobility, Exchange Mobility and Subgroup Consistent Mobility Measurement – US–German Mobility Measurements Revisited," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 08/543, Ghent University, Faculty of Economics and Business Administration.
    3. FLEURBAEY, Marc & SCHOKKAERT, Erik, 2011. "Equity in health and health care," LIDAM Discussion Papers CORE 2011026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 207-251, June.
    5. 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).
    6. Sonne-Schmidt, Christoffer & Tarp, Finn & Peter, Lars, 2011. "Ordinal multidimensional inequality: theory and application to the 2x2 case," MPRA Paper 72838, University Library of Munich, Germany.
    7. 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).

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    More about this item

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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