Comment on Shepsle's “On the Size of Winning Coalitions”

Butterworth, Robert Lyle

doi:10.1017/s0003055400117344

Cited by 2 publications

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“…We also plan to study the effect of abstention of some votes on the behavior of the weighted voting system. Further study pertaining to the structure and size of winning coalitions (Butterworth, 1971(Butterworth, , 1974Russell, 1976;Shepsle, 1974aShepsle, , 1974bNurmi, 1997;Axenovich and Roy, 2010;Kirsch and Langner, 2010), is warranted. Detailed comparison is required for the Banzhaf index and measures of importance in reliability (Freixas and Puente, 2002;Freixas and Pons, 2008;Kuo and Zhu, 2012;Zhu and Kuo, 2014).…”

Section: Discussionmentioning

confidence: 99%

Weighted voting systems: A threshold- Boolean perspective

Alturki

Rushdi

2016

J Engin Res

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W ö)«d «uE «Ë WO bMN « vM « s dO W c/Ë ¡UBI « w U U «-Ëoe W Ë"u*« X uB « rE VFK WD WO{U -WI dD rEM « Ác n u W K W U b u AEW oeUB ô« WO UL ô«Ë WO UO « WO ôu « ‰«Ëb « W ôb X uB « rEM Ÿ-U n Ë WL AE…dO J « rEMK UNLOLF sJ1 W u Ë W U oeu Ë s Ë ‰«Ëb « Ác ‰u …d u *« U uKF*« ¡«d s «dO n u « «c lH ABSTRACTWeighted voting systems play a crucial role in the investigation and modeling of many engineering structures and political and socio-economic phenomena. There is an urgent need to describe these systems in a simpli ed powerful mathematical way that can be generalized to systems of any size. An elegant description of voting systems is presented in terms of threshold Boolean functions. This description bene ts considerably from the wealth of information about these functions, and of the potpourri of algebraic and map techniques for handling them. The paper demonstrates that the prime implicants of the system threshold function are its Minimal Winning Coalitions (MWC). The paper discusses the Boolean derivative (Boolean difference) of the system threshold function with respect to each of its member components. The prime implicants of this Boolean difference can be used to deduce the winning coalitions (WC) in which the pertinent member cannot be dispensed with. Each of the minterms of this Boolean difference is a winning coalition in which this member plays a pivotal role. However, the coalition ceases to be winning if the member defects from it. Hence, the number of these minterms is identi ed as the Banzhaf index of voting power. The concepts introduced are illustrated with detailed demonstrative examples that also exhibit some of the known paradoxes of voting-system theory. Finally, the paper stresses the utility of threshold Boolean functions in the understanding, study, analysis, and design of weighted voting systems irrespective of size.

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Section: Discussionmentioning

confidence: 99%

Weighted voting systems: A threshold- Boolean perspective

Alturki

Rushdi

2016

J Engin Res

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Models of coalition behavior: Game theoretic, social psychological, and political perspectives.

Murnighan¹

1978

Psychological Bulletin

162

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This article reviews three classes of game theoretic solution concepts (solutions, subsolutions, and the core; bargaining set models; and the Shapley value), four social psychological models of coalition formation (minimum resource theory, minimum power theory, bargaining theory, and the weighted probability model), and three sets of political coalition models (minimum size, minimum range, and policy distance minimization). The research that has been conducted on characteristic function games, on experimental coalition situations involving more than three players, and on coalition governments is summarized and the models are evaluated. The advantages of collaboration among the three areas are discussed.

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Comment on Shepsle's “On the Size of Winning Coalitions”

Cited by 2 publications

References 0 publications

Weighted voting systems: A threshold- Boolean perspective

Weighted voting systems: A threshold- Boolean perspective

Models of coalition behavior: Game theoretic, social psychological, and political perspectives.

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