Power Indices Expressed in Terms of Minimal Winning Coalitions

15 Pages Posted: 31 May 2012

See all articles by Fabien Lange

Fabien Lange

University of Bordeaux - Montesquieu University - Bordeaux IV

Laszlo A. Koczy

Hungarian Academy of Sciences (HAS) - Research Centre for Economic and Regional Studies (HAS); Quantitative Social and Management Sciences Research Group, Budapest University of Technology and Economics

Date Written: May 30, 2012

Abstract

A voting situation is given by a set of voters and the rules of legislation that determine minimal requirements for a group of voters to pass a motion. A priori measures of voting power, such as the Shapley-Shubik index and the Banzhaf value, show the influence of the individual players in a voting situation and are calculated by looking at marginal contributions in a simple game consisting of winning and losing coalitions derived from the legislative rules.

We introduce a new way to calculate these measures directly from the set of minimal winning coalitions and derive explicit formulae for the Shapley-Shubik and Banzhaf values. This new approach logically appealing as it writes measures as functions of the rules of the legislation. For certain classes of games that arise naturally in applications the logical shortcut drastically simplifies the numerical calculations to obtain the indices. The technique generalises directly to all semivalues.

Keywords: Shapley-Shubik index, Banzhaf index, semivalue, minimal winning coalition, Möbius transform

JEL Classification: C71, D72

Suggested Citation

Lange, Fabien and Koczy, Laszlo A., Power Indices Expressed in Terms of Minimal Winning Coalitions (May 30, 2012). Available at SSRN: https://ssrn.com/abstract=2071084 or http://dx.doi.org/10.2139/ssrn.2071084

Fabien Lange

University of Bordeaux - Montesquieu University - Bordeaux IV ( email )

33608 Pessac Cedex
France

Laszlo A. Koczy (Contact Author)

Hungarian Academy of Sciences (HAS) - Research Centre for Economic and Regional Studies (HAS) ( email )

Budaörsi 45
Budapest, H-1112
Hungary

HOME PAGE: http://www.mtakti.hu/en/kutatok/laszlo-a-koczy/276/

Quantitative Social and Management Sciences Research Group, Budapest University of Technology and Economics ( email )

Magyar Tudósok krt. 2.
Budapest, 1117
Hungary

HOME PAGE: http://qsms.mokk.bme.hu/index.php/koczy/

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