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Measuring equality of opportunity by Shapley value


  • Giuseppe Pignataro

    () (Department of Economics, University of Bologna)


Equality of opportunity is a political ideal which requires that ex-ante inequalities, and only those inequalities, should be eliminated. Justice requires leveling the playing field by rendering everyone's opportunities equal in an appropriate sense, and then letting individual choices and their effects dictate further outcomes. In this paper we propose a methodology to decompose the path-independent Atkinson index of equality through Shapley value seeking for a measure of overall inequality produced by the marginal contributions of the opportunity and the responsibility component.

Suggested Citation

  • Giuseppe Pignataro, 2010. "Measuring equality of opportunity by Shapley value," Economics Bulletin, AccessEcon, vol. 30(1), pages 786-798.
  • Handle: RePEc:ebl:ecbull:eb-09-00665

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    References listed on IDEAS

    1. Daniele Checchi & Vito Peragine, 2010. "Inequality of opportunity in Italy," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 429-450, December.
    2. Cowell, F.A., 2000. "Measurement of inequality," Handbook of Income Distribution,in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 2, pages 87-166 Elsevier.
    3. Mercedes Sastre & Alain Trannoy, 2002. "Shapley inequality decomposition by factor components: Some methodological issues," Journal of Economics, Springer, vol. 9(1), pages 51-89, December.
    4. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    5. Mª Casilda Lasso de la Vega & Ana Marta Urrutia, 2003. "A new factorial decomposition for the atkinson measure," Economics Bulletin, AccessEcon, vol. 4(29), pages 1-12.
    6. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-685, November.
    7. 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.
    8. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-547, August.
    9. Chantreuil, F. & Trannoy, A., 1999. "Inequality Decomposition Values: the Trade-Off Between Marginality and Consistency," Papers 99-24, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    10. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
    11. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    12. repec:ebl:ecbull:v:4:y:2003:i:29:p:1-12 is not listed on IDEAS
    13. Mª Casilda Lasso de la Vega & Ana Marta Urrutia, 2005. "Path independent multiplicatively decomposable inequality measures," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 379-387, May.
    14. James E. Foster & Artyom A. Shneyerov, 1999. "A general class of additively decomposable inequality measures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 89-111.
    15. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
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    Cited by:

    1. John Creedy & Nicolas Hérault, 2011. "Decomposing Inequality and Social Welfare Changes: The Use of Alternative Welfare Metrics," Melbourne Institute Working Paper Series wp2011n08, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    2. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.
    3. A. Palestini & G. Pignataro, 2013. "A multi-factor inequality approach to a transfer scheme: the case of Common Agricultural Policy," Working Papers wp891, Dipartimento Scienze Economiche, Universita' di Bologna.

    More about this item


    Equality of opportunity; Shapley decomposition; Atkinson index; path independency.;

    JEL classification:

    • D6 - Microeconomics - - Welfare Economics
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty


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