Stable coalition structures and power indices for majority voting

Takaaki Abe

Journal of Public Economic Theory, 2022, vol. 24, issue 6, 1413-1432

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.

Date: 2022
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