The measurement of opportunity inequality: a cardinality-based approach
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.
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Volume (Year): 15 (1998)
Issue (Month): 2 ()
|Note:||Received: 2 May 1995 / Accepted: 11 October 1996|
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- Nitzan, Shmuel I. & Pattanaik, Prasanta K., 1984. "Median-based extensions of an ordering over a set to the power set: An axiomatic characterization," Journal of Economic Theory, Elsevier, vol. 34(2), pages 252-261, December.
- Prasanta K. PATTANAIK & Yongsheng XU, 1990. "On Ranking Opportunity Sets in Terms of Freedom of Choice," Discussion Papers (REL - Recherches Economiques de Louvain) 1990036, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Sen, Amartya, 1991. "Welfare, preference and freedom," Journal of Econometrics, Elsevier, vol. 50(1-2), pages 15-29, October.
- Bossert, Walter, 1989. "On the extension of preferences over a set to the power set: An axiomatic characterization of a quasi-ordering," Journal of Economic Theory, Elsevier, vol. 49(1), pages 84-92, October.
- Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
- Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
- Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
- Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
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