IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00389601.html
   My bibliography  Save this paper

Ethically robust comprisons of distributions of two individual attributes

Author

Listed:
  • Patrick Moyes

    (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Nicolas Gravel

Abstract

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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Patrick Moyes & Nicolas Gravel, 2007. "Ethically robust comprisons of distributions of two individual attributes," Post-Print hal-00389601, HAL.
    • Handle: RePEc:hal:journl:hal-00389601
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    2. 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.
    3. 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.
    4. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    5. Ian Crawford, 2005. "A nonparametric test of stochastic dominance in multivariate distributions," School of Economics Discussion Papers 1205, School of Economics, University of Surrey.
    6. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 199-209.
    7. 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.
    8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    9. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    10. 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.
    11. 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.
    12. 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.
    13. Vincenzo DenicolÔ, 1999. "A characterization of utilitarianism without the transitivity axiom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 273-278.
    14. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    15. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    16. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    17. Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 1-14.
    18. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    19. 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.
    20. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    21. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    22. 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(5), pages 849-866, December.
    23. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Banerjee, Asis Kumar, 2010. "A multidimensional Gini index," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 87-93, September.
    2. Claudio Zoli & Peter Lambert, 2012. "Sequential procedures for poverty gap dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 649-673, July.
    3. Benoît Tarroux, 2012. "Are equalization payments making Canadians better off? A two-dimensional dominance answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 19-44, March.
    4. Østerdal, Lars Peter, 2010. "The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1222-1228, November.
    5. 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.
    6. Nicolas Gravel & Patrick Moyes & Benoît 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, July.
    7. Nicolas Gravel & Abhiroop Mukhopadhyay, 2010. "Is India better off today than 15 years ago? A robust multidimensional answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 173-195, June.
    8. Pascaline Vincent & Frédéric Chantreuil & Benoït Tarroux, 2012. "Appraising the breakdown of unequal individuals in large French cities," Economics Working Paper Archive (University of Rennes & University of Caen) 201220, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    9. 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.
    10. 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).
    11. 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).
    12. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    13. 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.
    14. 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).
    15. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2008. "Ordinal Comparison of Multidimensional Deprivation: theory and application," Discussion Papers 08-33, University of Copenhagen. Department of Economics.
    16. Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics.
    17. 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.
    18. Benoît Tarroux, 2012. "Appraising two-Dimensional Inequality: A Questionnaire-Experimental Approach," Economics Working Paper Archive (University of Rennes & University of Caen) 201216, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    19. Patrick MOYES, 2008. "Poverty Measurement in Economics (In French)," Cahiers du GREThA (2007-2019) 2008-06, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicolas Gravel & Abhiroop Mukhopadhyay, 2010. "Is India better off today than 15 years ago? A robust multidimensional answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 173-195, June.
    2. Nicolas Gravel & Patrick Moyes & Benoît 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, July.
    3. 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.
    4. Benoît Tarroux, 2012. "Are equalization payments making Canadians better off? A two-dimensional dominance answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 19-44, March.
    5. Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2017. "Multidimensional Pigou–Dalton transfers and social evaluation functions," Theory and Decision, Springer, vol. 83(4), pages 573-590, December.
    6. 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.
    7. 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).
    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. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 2020. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 645-686, December.
    10. Elisa Pagani, 2015. "Certainty Equivalent: Many Meanings of a Mean," Working Papers 24/2015, University of Verona, Department of Economics.
    11. 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.
    12. Frank A Cowell & Martyna Kobus & Radoslaw Kurek, 2017. "Welfare and Inequality Comparisons for Uni- and Multi-dimensional Distributions of Ordinal Data," STICERD - Public Economics Programme Discussion Papers 31, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. 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.
    14. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    15. Zhong, Hai, 2009. "A multivariate analysis of the distribution of individual's welfare in China: What is the role of health?," Journal of Health Economics, Elsevier, vol. 28(6), pages 1062-1070, December.
    16. 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).
    17. 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).
    18. 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.
    19. Chakravarty, Satya R. & Sarkar, Palash, 2022. "A synthesis of local and effective tax progressivity measurement," MPRA Paper 115180, University Library of Munich, Germany.
    20. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2013. "On the Measurement of the (Multidimensional) Inequality of Health Distributions," Research on Economic Inequality, in: Health and Inequality, volume 21, pages 111-129, Emerald Group Publishing Limited.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00389601. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.