A note on monotonic power indices, smaller coalitions and new members

Dominik Karos*

*Corresponding author for this work

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Brams' paradox of new members and Shenoy's paradox of smaller coalitions are, in a sense, equivalent. They are both implied by the monotonicity of a power index: while the first is exhibited on every simple game that is not strong, the latter can be observed on every simple game in which players are not almost symmetric. For the Shapley-Shubik index, this symmetry condition is not only necessary but also sufficient to avoid the paradox of smaller coalitions.

Original languageEnglish
Pages (from-to)89-100
Number of pages12
JournalTheory and Decision
Issue number1
Publication statusPublished - Jun 2016


  • Paradox of smaller coalitions
  • Paradox of new members
  • Monotonic power indices

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