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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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Publisher Info
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. 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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  3. 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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  4. Dimitrov, D. & Arlegi, R., 2004. "On procedural freedom of choice," Discussion Paper 9, Tilburg University, Center for Economic Research. [Downloadable!]
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  5. 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!]
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  7. E. Ooghe & E. Schokkaert & D. Van De Gaer, 2004. "Equality of opportunity versus equality of opportunity sets," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 04/240, Ghent University, Faculty of Economics and Business Administration. [Downloadable!]
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  8. Ricardo Arlegi, 2005. "Freedom Of Choice And Conflict Resolution," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0502, Departamento de Economía - Universidad Pública de Navarra. [Downloadable!]
  9. Vito Peragine & Laura Serlenga, 2007. "Higher Education and Equality of Opportunity in Italy," IZA Discussion Papers 3163, Institute for the Study of Labor (IZA). [Downloadable!]
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  10. 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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  11. 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)
  12. 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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  13. 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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