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Generalized Coleman-Shapley Indices And Total-Power Monotonicity

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  • Ori Haimanko

    (BGU)

Abstract

We introduce a new axiom for power indices, which requires the total (additively aggregated) power of the voters to be nondecreasing in response to an expansion of the set of winning coalitions; the total power is thereby reflecting an increase in the collective power that such an expansion creates. It is shown that total-power monotonic indices that satisfy the standard semivalue axioms are probabilistic mixtures of generalized Coleman-Shapley indices, where the latter concept extends, and is inspired by, the notion introduced in Casajus and Huettner (Public choice, forthcoming, 2019). Generalized Coleman-Shapley indices are based on a version of the random-order pivotality that is behind the Shapley-Shubik index, combined with an assumption of random participation by players.
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  • Ori Haimanko, 2018. "Generalized Coleman-Shapley Indices And Total-Power Monotonicity," Working Papers 1813, Ben-Gurion University of the Negev, Department of Economics.
    • Handle: RePEc:bgu:wpaper:1813
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    References listed on IDEAS

    as
    1. Haimanko, Ori, 2018. "The axiom of equivalence to individual power and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 108(C), pages 391-400.
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    7. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
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