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Generalized Coleman-Shapley indices and total-power monotonicity

Ori Haimanko

International Journal of Game Theory, 2020, vol. 49, issue 1, No 13, 299-320

Abstract: 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.

Keywords: Simple games; Voting power; Shapley-Shubik index; Banzhaf index; Coleman-Shapley index; Semivalues; Power of collectivity to act; Total-power monotonicity axiom; Probabilistic mixtures; C71; D72 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00182-019-00692-2

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Handle: RePEc:spr:jogath:v:49:y:2020:i:1:d:10.1007_s00182-019-00692-2