Generalized Coleman-Shapley indices and total-power monotonicity

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Pages (from-to)299-320
Number of pages22
JournalInternational Journal of Game Theory
Issue number1
StatePublished - 1 Mar 2020


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

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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