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Ranking Distributions of an Ordinal Attribute

Author

Listed:
  • Nicolas Gravel

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Brice Magdalou

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

  • Patrick Moyes

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

Abstract

This paper establishes foundational equivalences between alternative criteria for comparing distributions of an ordinally measurable attribute. A first criterion is associated with the possibility of going from distribution to the other by a finite sequence of two elementary operations: increments of the attribute and Hammond transfers. The later transfers are like the famous Pigou-Dalton ones, but without the requirement - that would be senseless in an ordinal setting - that the "amount" transferred from the "rich" to the "poor" is fixed. A second criterion is a new easy-to-use statistical criterion associated to a specifically weighted recursion on the cumulative density of the distribution function. A third criterion is that resulting from the comparison of numerical values assigned to distributions by a large class of additively separable social evaluation functions. Dual versions of these criteria are also considered and alternative equivalence results are established. Illustrations of the criteria are also provided.

Suggested Citation

  • Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2015. "Ranking Distributions of an Ordinal Attribute," Working Papers halshs-01082996, HAL.
  • Handle: RePEc:hal:wpaper:halshs-01082996
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01082996v2
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    Cited by:

    1. Magdalou, Brice, 2021. "A model of social welfare improving transfers," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2017. "Hammond’s Equity Principle and the Measurement of Ordinal Inequalities," AMSE Working Papers 1703, Aix-Marseille School of Economics, France.
    3. Frank A. Cowell & Emmanuel Flachaire, 2017. "Inequality with Ordinal Data," Economica, London School of Economics and Political Science, vol. 84(334), pages 290-321, April.
    4. Martyna Kobus & Radosław Kurek, 2019. "Multidimensional polarization for ordinal data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(3), pages 301-317, September.
    5. Marc Fleurbaey & François Maniquet, 2019. "Well-being measurement with non-classical goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 765-786, October.
    6. Stephen P. Jenkins, 2021. "Inequality Comparisons with Ordinal Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(3), pages 547-563, September.
    7. 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.
    8. Stephen P. Jenkins, 2020. "Better off? Distributional comparisons for ordinal data about personal well-being," New Zealand Economic Papers, Taylor & Francis Journals, vol. 54(3), pages 211-238, September.
    9. Ramses H. Abul Naga, 2018. "Measurement of inequality with a finite number of pay states: the majorization set and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 99-123, January.
    10. Suman Seth and Gaston Yalonetzky, 2018. "Assessing Deprivation with Ordinal Variables: Depth Sensitivity and Poverty Aversion," OPHI Working Papers ophiwp123.pdf, Queen Elizabeth House, University of Oxford.
    11. 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.
    12. Suman Seth & Gaston Yalonetzky, 2021. "Assessing Deprivation with an Ordinal Variable: Theory and Application to Sanitation Deprivation in Bangladesh," The World Bank Economic Review, World Bank, vol. 35(3), pages 793-811.
    13. Rolf Aaberge & Eugenio Peluso & Henrik Sigstad, 2015. "The dual approach for measuring. Multidimesional deprivation and poverty," Discussion Papers 820, Statistics Norway, Research Department.
    14. Sandip Sarkar & Sattwik Santra, 2020. "Extending the approaches to polarization ordering of ordinal variables," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(3), pages 421-440, September.
    15. Martyna Kobus & Olga Półchłopek & Gaston Yalonetzky, 2019. "Inequality and Welfare in Quality of Life Among OECD Countries: Non-parametric Treatment of Ordinal Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(1), pages 201-232, May.
    16. Valérie Bérenger & Jacques Silber, 2022. "On the Measurement of Happiness and of its Inequality," Journal of Happiness Studies, Springer, vol. 23(3), pages 861-902, March.
    17. Alejandro Corvalan, 2018. "How to rank rankings? Group performance in multiple-prize contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 361-380, August.

    More about this item

    Keywords

    ordinal; qualitative; health; inequality; Hammond transfers; increments; dominance;
    All these keywords.

    JEL classification:

    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I1 - Health, Education, and Welfare - - Health
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

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