Power indices in a discretely proportional representative system with a large number of voters
type: Item
instance of: scholarly article
title: Power indices in a discretely proportional representative system with a large number of voters
zbMATH Open document ID: 0546.90001
DOI: 10.1016/0165-4896(83)90049-5
published in: Mathematical Social Sciences
publication date: 1983-01-01T00:00:00Z
review text: To evaluate the power of voters in a political system, indices introduced by Shapley and Shubik as well as Banzhaf are used in the literature. The author applies these indices to a certain representative system, modeling the elections to the Japanese House of Representatives. Having developed a game-theoretic formulation of the representative system, the Shapley- Shubik and the Banzhaf index are computed using Owen's 1972- approximation. Then, a simple example of the representative system is presented. Applied to this example, the Shapley-Shubik and the Banzhaf index are shown to have considerable deficiences. The introduction of an appropriate modification of the indices is put off to a future paper.
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91A80
zbMATH DE Number: 3870964
zbMATH Keywords: Banzhaf index
zbMATH Keywords: Shapley-Shubik index
zbMATH Keywords: power of voters
zbMATH Keywords: political system
zbMATH Keywords: Japanese House of Representatives
author: Shigeo Muto
reviewed by: Alfred Endres
MaRDI profile type: Publication
full work available at URL: 0165-4896(83)90049-5
OpenAlex ID: W2038025012
cites work: Q3661354
cites work: Multilinear Extensions of Games
cites work: Q3948907
cites work: Q3707792
description: scientific article; zbMATH DE number 3870964