Egalitarian property for power indices |
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Authors: | Josep Freixas Dorota Marciniak |
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Institution: | 1. Department of Applied Mathematics III and High Engineering School of Manresa, Technical University of Catalonia, Barcelona, Spain 2. National Institute of Telecommunications, Ul. Szachowa 1, 04-894, Warsaw, Poland 3. Centre for Research and Studies in Sociology, CIES-ISCTE-IUL, Lisbon, Portugal
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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. |
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