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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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    Cited by:

    1. Rebeca Echávarri & Iñaki Permanyer, 2008. "Ranking profiles of capability sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 521-535, October.
    2. 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.
    3. Francisco H. G. Ferreira & Vito Peragine, 2015. "Equality of opportunity: Theory and evidence," Working Papers 359, ECINEQ, Society for the Study of Economic Inequality.
    4. Donal O'Neill & Olive Sweetman & Dirk van de gaer, 1999. "Equality 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.
    5. Egozcue, Martin & Wong, Wing-Keung, 2010. "Gains from diversification on convex combinations: A majorization and stochastic dominance approach," European Journal of Operational Research, Elsevier, vol. 200(3), pages 893-900, February.
    6. Arlegi, R. & Dimitrov, D.A., 2004. "On Procedural Freedom of Choice," Discussion Paper 2004-9, Tilburg University, Center for Economic Research.
    7. John Weymark, 2003. "Generalized Gini Indices of Equality of Opportunity," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 5-24, April.
    8. Savaglio, Ernesto & Vannucci, Stefano, 2007. "Filtral preorders and opportunity inequality," Journal of Economic Theory, Elsevier, vol. 132(1), pages 474-492, January.
    9. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Erwin Ooghe & Erik Schokkaert & Dirk gaer, 2007. "Equality of Opportunity versus Equality of Opportunity Sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(2), pages 209-230, February.
    11. Vito Peragine, 2004. "Measuring and implementing equality of opportunity for income," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(1), pages 187-210, February.
    12. Peragine, Vito & Serlenga, Laura, 2007. "Higher Education and Equality of Opportunity in Italy," IZA Discussion Papers 3163, Institute for the Study of Labor (IZA).
    13. Marco, Mariotti & Roberto, Veneziani, 2012. "Opportunities as chances: maximising the probability that everybody succeeds," MPRA Paper 41884, University Library of Munich, Germany.
    14. John E. Roemer & Alain Trannoy, 2016. "Equality of Opportunity: Theory and Measurement," Journal of Economic Literature, American Economic Association, vol. 54(4), pages 1288-1332, December.
    15. Jorge Alcalde-Unzu & Miguel Ballester, 2010. "On ranking opportunity distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(1), pages 3-31, January.
    16. François Maniquet, 2004. "On the equivalence between welfarism and equality of opportunity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 127-147, August.
    17. Jorge Alcalde-Unzu & Miguel Ballester, 2012. "Ranking opportunity profiles through dependent evaluation of policies," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(4), pages 471-487, December.
    18. Laurence Kranich, 2009. "Measuring opportunity inequality with monetary transfers," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(4), pages 371-385, December.
    19. Vitorocco Peragine, "undated". "Responsibility Compensation and Income Distribution," Discussion Papers 98/13, Department of Economics, University of York.
    20. 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.
    21. Corchon, Luis C. & Iturbe-Ormaetxe, Inigo, 2001. "A Proposal to Unify Some Concepts in the Theory of Fairness," Journal of Economic Theory, Elsevier, vol. 101(2), pages 540-571, December.
    22. Guo, Xu & Wong, Wing-Keung, 2016. "Multivariate Stochastic Dominance for Risk Averters and Risk Seekers," MPRA Paper 70637, University Library of Munich, Germany.
    23. Peragine, Vitorocco, 2002. "Opportunity egalitarianism and income inequality," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 45-64, September.
    24. Vito Peragine, 2004. "Ranking Income Distributions According to Equality of Opportunity," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(1), pages 11-30, April.
    25. Stefano Vannucci, 2013. "A characterization of height-based extensions of principal filtral opportunity rankings," REVISTA CUADERNOS DE ECONOMÍA, UN - RCE - CID, December.

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