Generalized Coleman-Shapley indices and total-power monotonicity

  • Ori HaimankoEmail author
Original Paper


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.


Simple games Voting power Shapley-Shubik index Banzhaf index Coleman-Shapley index Semivalues Power of collectivity to act Total-power monotonicity axiom Probabilistic mixtures 

JEL classification numbers

C71 D72 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsBen-Gurion University of the NegevBeer ShevaIsrael

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