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Stable coalition structures and power indices for majority voting
Author(s) -
Abe Takaaki
Publication year - 2022
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/jpet.12574
Subject(s) - axiom , core (optical fiber) , mathematical economics , voting , stability (learning theory) , power (physics) , power index , outcome (game theory) , set (abstract data type) , a priori and a posteriori , property (philosophy) , game theory , economics , mathematics , computer science , political science , law , machine learning , politics , telecommunications , philosophy , physics , geometry , epistemology , quantum mechanics , programming language
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.