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The measurement of opportunity inequality: a cardinality-based approach

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  • Efe A. Ok

    (Department of Economics, New York University, 269 Mercer Street, New York, NY 10003, USA)

  • Laurence Kranich

    (Departamento de Economia, Universidad Carlos III de Madrid, Calle Madrid 126, E-28903 Getafe , Spain)

Abstract

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on a given ranking of individual opportunity sets, we define the notion of an equalizing transformation. Then, assuming that the opportunity sets are ranked according to the cardinality ordering, we formulate the analogues of the notions of the Lorenz partial ordering, equalizing (Dalton) transfers, and inequality averse social welfare functions - concepts which play a central role in the literature on income inequality. Our main result is a cardinality-based analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of rank preserving equalizations, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functions. In addition, we characterize the smallest monotonic and transitive extension of our cardinality-based Lorenz inequality ordering.

Suggested Citation

  • Efe A. Ok & Laurence Kranich, 1998. "The measurement of opportunity inequality: a cardinality-based approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 263-287.
    • Handle: RePEc:spr:sochwe:v:15:y:1998:i:2:p:263-287
    Note: Received: 2 May 1995 / Accepted: 11 October 1996
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