Composition independence in compound games: a characterization of the Banzhaf power index and the Banzhaf value

  • Ori HaimankoEmail author
Original Paper


We introduce the axiom of composition independence for power indices and value maps. In the context of compound (two-tier) voting, the axiom requires the power attributed to a voter to be independent of the second-tier voting games played in all constituencies other than that of the voter. We show that the Banzhaf power index is uniquely characterized by the combination of composition independence, four semivalue axioms (transfer, positivity, symmetry, and dummy), and a mild efficiency-related requirement. A similar characterization is obtained as a corollary for the Banzhaf value on the space of all finite games (with transfer replaced by additivity).


Simple games Compound games Banzhaf power index Banzhaf value Composition property Semivalues Transfer Symmetry Positivity Dummy 

JEL Classification

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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