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Generalized Coleman-Shapley indices and total-power monotonicity

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  • Ori Haimanko

    (Ben-Gurion University of the Negev)

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.

Suggested Citation

  • Ori Haimanko, 2020. "Generalized Coleman-Shapley indices and total-power monotonicity," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 299-320, March.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:1:d:10.1007_s00182-019-00692-2
    DOI: 10.1007/s00182-019-00692-2
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