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The measurement of opportunity inequality: a cardinality-based approach

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Author Info
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)

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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.

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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 15 (1998)
Issue (Month): 2 ()
Pages: 263-287
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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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  2. Rebeca Echávarri & Iñaki Permanyer, 2008. "Ranking profiles of capability sets," Social Choice and Welfare, Springer, vol. 31(3), pages 521-535, October. [Downloadable!] (restricted)
  3. Vito Peragine & Ernesto Savaglio & Stefano Vannucci, 2008. "Poverty Rankings of Opportunity Profiles," Department of Economics University of Siena 548, Department of Economics, University of Siena. [Downloadable!]
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  4. Iñigo Iturbe Ormaetxe & Luis Corchón, 1997. "- A Proposal To Unify Some Concepts In The Theory Of Fairness," Working Papers. Serie AD 1997-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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  5. John A. Weymark, 2001. "Generalized Gini Indices of Equality of Opportunity," Working Papers 0114, Department of Economics, Vanderbilt University, revised Jun 2002. [Downloadable!]
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  6. Laura Serlenga & Vito Peragine, 2007. "Higher education and equality of opportunity in Italy," Working Papers 79, ECINEQ, Society for the Study of Economic Inequality. [Downloadable!]
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  7. BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  8. Francois Maniquet, 2002. "On the Equivalence between Welfarism and Equality of Opportunity," Economics Working Papers 0022, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  9. Erwin Ooghe & Erik Schokkaert & Dirk gaer, 2007. "Equality of Opportunity versus Equality of Opportunity Sets," Social Choice and Welfare, Springer, vol. 28(2), pages 209-230, February. [Downloadable!] (restricted)
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  10. Vitorocco Peragine, . "Measuring and Implementing Equality of Opportunity for Income," Discussion Papers 98/11, Department of Economics, University of York. [Downloadable!]
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  11. Dimitrov, D. & Arlegi, R., 2004. "On procedural freedom of choice," Discussion Paper 9, Tilburg University, Center for Economic Research. [Downloadable!]
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  12. Vito Peragine, 2004. "Ranking Income Distributions According to Equality of Opportunity," Journal of Economic Inequality, Springer, vol. 2(1), pages 11-30, April. [Downloadable!] (restricted)
  13. Donal O'Neill & Olive Sweetman & Dirk van de gaer, 1999. "Equiality of Opportunity and Kernel Density Estimation: An Application to Intergenerational Mobility," Economics, Finance and Accounting Department Working Paper Series n950999, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth. [Downloadable!]
  14. Vitorocco Peragine, . "Responsibility Compensation and Income Distribution," Discussion Papers 98/13, Department of Economics, University of York. [Downloadable!]
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