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Ranking opportunity profiles through dependent evaluation of policies


Rankings to evaluate opportunity distributions present in most of the literature judge a policy (change from one distribution of opportunities to another) on the basis of the changes created and, thus, independently of the original situation. This paper proposes a group of axioms capturing the idea that rankings of equality of opportunities might consider not only the changes promoted, but also the initial situation in society. The combination of this group of axioms with other well-established properties enables us to characterize two families of new opportunity distribution rankings. The first family weighs each individual’s percentage share in the total number of opportunities, while the second weighs opportunities depending on how many agents have them available.

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  1. 1.

    Alcalde-Unzu, J., Arlegi, R., Nieto, J.: Cardinality-based Equality of opportunities. Rev. Econ. Des. 10, 285–304 (2007)

    Google Scholar 

  2. 2.

    Alcalde-Unzu, J., Ballester, M.: On the axiomatic distribution of opportunities. Soc. Choice Welf. 34, 3–31 (2010)

    Article  Google Scholar 

  3. 3.

    Arneson, R.: Equality and equality of opportunity for welfare. Philos. Stud. 56, 77–93 (1989)

    Article  Google Scholar 

  4. 4.

    Atkinson, A.B.: Social Justice and Public Policy. The M.I.T. Press (1983)

  5. 5.

    Barbera, S., Jackson, M.: Maximin, leximin and the protective criterion: characterizations and comparisons. J. Econ. Theory 46, 34–44 (1988)

    Article  Google Scholar 

  6. 6.

    Bossert, W., Fleuerbaey, M., van de Gaer, D.: Responsibility, talent, and compensation: a second-best analysis. Rev. Econ. Des. 4, 35–55 (1999)

    Google Scholar 

  7. 7.

    Dardanoni, V.: Measuring social mobility. J. Econ. Theory 61, 372–394 (1993)

    Article  Google Scholar 

  8. 8.

    Dworkin, R.: What is equality? Part 1: equality of welfare. Philos. Public Aff. 10, 185–246 (1981)

    Google Scholar 

  9. 9.

    Dworkin, R.: What is equality? Part 1: equality of resources. Philos. Public Aff. 10, 283–345 (1981)

    Google Scholar 

  10. 10.

    Echávarri, R., Permanyer, I.: Ranking profiles of capability sets. Soc. Choice Welf. 31, 521–535 (2008)

    Article  Google Scholar 

  11. 11.

    Elster, J.: Sour grapes-utilitarianism and the genesis of wants. In: Sen, A.K., Williams, B. (eds) Utilitarianism and Beyond. Cambridge University Press, Cambridge (1982)

    Google Scholar 

  12. 12.

    Fleurbaey, M.: Living standards and capabilities: equal values or equal sets? Anal. Krit. 29, 226–234 (2007)

    Google Scholar 

  13. 13.

    Herrero, C.: Equitable opportunities: an extension. Econ. Lett. 55, 91–95 (1997)

    Article  Google Scholar 

  14. 14.

    Herrero, C., Iturbe-Ormaetxe, I., Nieto, J.: Ranking opportunity profiles on the basis of the common opportunities. Math. Soc. Sci. 35, 273–289 (1998)

    Article  Google Scholar 

  15. 15.

    King, M.: An index of inequality: with applications to horizontal equity and social mobility. Econometrica 51, 99–115 (1983)

    Article  Google Scholar 

  16. 16.

    Kranich, L.: Equitable opportunities: an axiomatic approach. J. Econ. Theory 71, 131–147 (1996)

    Article  Google Scholar 

  17. 17.

    Ok, E.A.: On opportunity inequality measurement. J. Econ. Theory 77, 300–329 (1997)

    Article  Google Scholar 

  18. 18.

    Ok, E.A., Kranich, L.: The measurement of opportunity inequality: a cardinality-based approach. Soc. Choice Welf. 15, 263–287 (1998)

    Article  Google Scholar 

  19. 19.

    Pattanaik, P., Xu, Y.: On ranking opportunity sets in terms of freedom of choice. Rech. Econ. Louvain 56, 383–390 (1990)

    Google Scholar 

  20. 20.

    Peragine, V.: The distribution and the redistribution of opportunities. J. Econ. Surv. 13, 37–69 (1999)

    Article  Google Scholar 

  21. 21.

    Rawls, J.: A Theory of Justice. Harvard University Press, Cambridge, Massachusetts (1971)

    Google Scholar 

  22. 22.

    Savaglio, E., Vanucci, S.: Filtral preorders and opportunity inequality. J. Econ. Theory 132, 474–492 (2007)

    Article  Google Scholar 

  23. 23.

    Sen, A.K.: Commodities and Capabilities. North-Holland, Amsterdam (1985)

    Google Scholar 

  24. 24.

    Sen, A.K.: Welfare, preference and freedom. J. Econom. 50, 15–29 (1991)

    Article  Google Scholar 

  25. 25.

    Van de Gaer, D., Schokkaert, E., Martinez, M.: Three meanings of intergenerational mobility. Economica 68, 519–537 (2001)

    Article  Google Scholar 

  26. 26.

    Weymark, J.: Generalized Gini indices of equality of opportunity. Journal of Economic Inequality 1, 5–24 (2003)

    Article  Google Scholar 

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Correspondence to Jorge Alcalde-Unzu.

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Alcalde-Unzu, J., Ballester, M.A. Ranking opportunity profiles through dependent evaluation of policies. J Econ Inequal 10, 471–487 (2012).

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  • Opportunity profiles
  • Advantage
  • Equality
  • Evaluation of policies