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Ranking distributions of an ordinal attribute


  • Nicolas Gravel
  • Brice Magdalou
  • Patrick Moyes


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," Working Papers 14-13, LAMETA, Universtiy of Montpellier, revised Nov 2014.
  • Handle: RePEc:lam:wpaper:14-13

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    Cited by:

    1. 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.
    2. 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.
    3. Brice Magdalou, 2018. "A model of social welfare improving transfers," Working Papers hal-01975452, HAL.
    4. 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.
    5. repec:bla:econom:v:84:y:2017:i:334:p:290-321 is not listed on IDEAS
    6. Rolf Aaberge & Eugenio Peluso & Henrik Sigstad, 2015. "The dual approach for measuring. Multidimesional deprivation and poverty," Discussion Papers 820, Statistics Norway, Research Department.
    7. repec:spr:joecth:v:65:y:2018:i:1:d:10.1007_s00199-016-1011-2 is not listed on IDEAS
    8. 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.
    9. Brice Magdalou, 2018. "A model of social welfare improving transfers," Working Papers hal-01975452, HAL.
    10. repec:spr:sochwe:v:51:y:2018:i:2:d:10.1007_s00355-018-1120-x is not listed on IDEAS

    More about this item

    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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