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Ethically robust comparisons of bidimensional distributions with an ordinal attribute

Author

Listed:
  • Patrick Moyes

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

  • Nicolas Gravel

Abstract

We provide foundations for robust normative evaluation of distributions of two attributes, one of which is cardinally measurable and transferable between individuals and the other is ordinal and non-transferable. The result that we establish takes the form of an analogue to the standard Hardy-Littlewood-Polya theorem for distributions of one cardinal attribute. More specifically, we identify the transformations of the distributions which guarantee that social welfare increases according to utilitarian unanimity provided that the utility function is concave in the cardinal attribute and that its marginal utility with respect to the same attribute is non-increasing in the ordinal attribute. We establish that this unanimity ranking of the distributions is equivalent to the ordered poverty gap quasi-ordering introduced by Bourguignon [12]. Finally, we show that, if one distribution dominates another according to the ordered poverty gap criterion, then the former can be derived from the latter by means of an appropriate and finite sequence of such transformations.

Suggested Citation

  • Patrick Moyes & Nicolas Gravel, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Post-Print hal-00796050, HAL.
    • Handle: RePEc:hal:journl:hal-00796050
    DOI: 10.1016/j.jet.2012.01.001
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    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • 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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