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Stable coalition structures and power indices for majority voting

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  • Takaaki Abe

Abstract

An (n,k)‐game is a voting game in which each player has exactly one vote, and decisions are made by at least k affirmative votes of the n players. A power index shows the a priori power of the n voters. The purpose of this paper is to show what axioms of power indices generate stable coalition structures for each (n,k)‐game. Using the stability notion of the core, we show that a coalition structure containing a minimal winning coalition is stable for a wide range of general power indices satisfying a set of axioms, such as the Shapley–Shubik, Banzhaf, normalized Banzhaf, and Deegan–Packel power indices. Moreover, we also show that a coalition structure that represents a two‐party system can be stable if the two large parties are close enough in size. Some unstable coalition structures are also analyzed.

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  • Takaaki Abe, 2022. "Stable coalition structures and power indices for majority voting," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1413-1432, December.
    • Handle: RePEc:bla:jpbect:v:24:y:2022:i:6:p:1413-1432
    DOI: 10.1111/jpet.12574
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    References listed on IDEAS

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