The fundamental theorem of voting schemes
type: Item
instance of: scholarly article
title: The fundamental theorem of voting schemes
zbMATH Open document ID: 0839.90142
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-05-13T00:00:00Z
review text: A coalition \(A\subseteq V\) is said to be blocking (in \(S\)) if \(\overline A\not\in S\). The set of all blocking coalitions is denoted \(S^*\), and is called the dual of \(S\), since \((S^*)^*= S\). A game \(S\) is simple if \(A\in S\) (\(A\) wins) implies \(\overline A\not\in S\) (\(A\) blocks); i.e. \(S\subseteq S^*\). Conversely, a game \(S\) is strong if \(\overline A\not\in S\) (\(A\) blocks) implies \(A\in S\) (\(A\) wins); i.e. \(S^*\subseteq S\). The main result of this paper is the proof of the ``Fundamental Theorem'' of strong simple games, namely, all full strong simple games have unique decompositions into prime strong-simple-games.
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B12
zbMATH DE Number: 842834
zbMATH Keywords: blocking coalitions
zbMATH Keywords: strong simple games
author: Daniel E. Loeb
MaRDI profile type: Publication
full work available at URL: jcta.1996.0006
OpenAlex ID: W2013061485
DOI: 10.1006/JCTA.1996.0006
description: scientific article; zbMATH DE number 842834