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Egalitarian property for power indices

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Listed:
  • Josep Freixas

  • Dorota Marciniak

Abstract

In this study, we introduce and examine the Egalitarian property for some power indices on the class of simple games. This property means that after intersecting a game with a symmetric or anonymous game the difference between the values of two comparable players does not increase. We prove that the Shapley–Shubik index, the absolute Banzhaf index, and the Johnston score satisfy this property. We also give counterexamples for Holler, Deegan–Packel, normalized Banzhaf and Johnston indices. We prove that the Egalitarian property is a stronger condition for efficient power indices than the Lorentz domination. Copyright The Author(s) 2013

Suggested Citation

  • Josep Freixas & Dorota Marciniak, 2013. "Egalitarian property for power indices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 207-227, January.
    • Handle: RePEc:spr:sochwe:v:40:y:2013:i:1:p:207-227
    DOI: 10.1007/s00355-011-0593-7
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    References listed on IDEAS

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    1. Carreras, Francesc & Freixas, Josep & Puente, Maria Albina, 2003. "Semivalues as power indices," European Journal of Operational Research, Elsevier, vol. 149(3), pages 676-687, September.
    2. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    3. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    4. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    5. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    6. Josep Freixas, 2010. "On ordinal equivalence of the Shapley and Banzhaf values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 513-527, October.
    7. Carreras, Francesc & Freixas, Josep, 2004. "A power analysis of linear games with consensus," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 207-221, September.
    8. R J Johnston, 1978. "On the Measurement of Power: Some Reactions to Laver," Environment and Planning A, , vol. 10(8), pages 907-914, August.
    9. Carreras, Francesc & Freixas, Josep, 2008. "On ordinal equivalence of power measures given by regular semivalues," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 221-234, March.
    10. Laruelle, Annick & Valenciano, Federico, 2002. "Inequality among EU citizens in the EU's Council decision procedure," European Journal of Political Economy, Elsevier, vol. 18(3), pages 475-498, September.
    11. repec:cup:apsrev:v:63:y:1969:i:01:p:40-56_26 is not listed on IDEAS
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