Ethically robust comparisons of bidimensional distributions with an ordinal attribute

Nicolas Gravel () and Patrick Moyes ()

Journal of Economic Theory, 2012, vol. 147, issue 4, 1384-1426

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–Pólya 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.

Keywords: Normative analysis; Utilitarianism; Bidimensional stochastic dominance; Inequality reducing transformations (search for similar items in EconPapers)
JEL-codes: D30 D63 I31 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (36)

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Related works:
Working Paper: Ethically robust comparisons of bidimensional distributions with an ordinal attribute (2012)
Working Paper: Ethically Robust Comparisons of Bidimensional Distributions with an Ordinal Attribute (2011)
Working Paper: Ethically robust comparisons of bidimensional distributions with an ordinal attribute (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:147:y:2012:i:4:p:1384-1426

DOI: 10.1016/j.jet.2012.01.001

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