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Ranking Distributions of an Ordinal Attribute

Author

Listed:
  • Nicolas Gravel

    (Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS)

  • Brice Magdalou

    (Université de Montpellier 1 & LAMETA)

  • Patrick Moyes

    (CNRS, GRETHA, Université Montesquieu (Bordeaux 4))

Abstract

This paper establishes an equivalence between three incomplete rankings of distributions of an ordinally measurable attribute. The first ranking is that associated with the possibility of going from distribution to the other by a finite sequence of two elementary operations: increments of the attribute and the so-called Hammond transfer. The later transfer is like the Pigou-Dalton transfer, but without the requirement - that would be senseless in an ordinal setting - that the "amount" transferred from the "rich" to the "poor" is fixed. The second ranking is an easy-to-use statistical criterion associated to a specifically weighted recursion on the cumulative density of the distribution function. The third ranking is that resulting from the comparison of numerical values assigned to distributions by a large class of additively separable social evaluation functions. Illustrations of the criteria are also provided.

Suggested Citation

  • Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2014. "Ranking Distributions of an Ordinal Attribute," AMSE Working Papers 1450, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:1450
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Rolf Aaberge & Eugenio Peluso & Henrik Sigstad, 2015. "The dual approach for measuring. Multidimesional deprivation and poverty," Discussion Papers 820, Statistics Norway, Research Department.
    6. 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.
    7. 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.
    8. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2017. "Hammond’s Equity Principle and the Measurement of Ordinal Inequalities," Working Papers halshs-01430838, HAL.
    9. Magdalou, Brice, 2021. "A model of social welfare improving transfers," Journal of Economic Theory, Elsevier, vol. 196(C).
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    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. 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.
    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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