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Egalitarian property for power indices

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  • 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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