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L.S. Penrose's limit theorem : proof of some special cases

Lindner, Ines and Machover, Moshé (2004) L.S. Penrose's limit theorem : proof of some special cases. Mathematical Social Sciences, 47 (1). pp. 37-49. ISSN 0165-4896

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Abstract

LS Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf index’). His limit theorem – which is implicit in Penrose (1952) and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while the quota is pegged at half the total weight, then – under certain conditions – the ratio between the voting powers (as measured by him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined weighted voting games, other values of the quota, and other measures of voting power. We provide proofs for some special cases.

Item Type: Article
Official URL: http://www.elsevier.com/locate/mss
Additional Information: The authors gratefully acknowledge that work on this paper was partly supported by the Leverhulme Trust (Grant F/07-004m). Published 2004 © Elsevier B.V.
Library of Congress subject classification: J Political Science > JC Political theory
Sets: Research centres and groups > Centre for Philosophy of Natural and Social Science (CPNSS)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 22 Dec 2005
URL: http://eprints.lse.ac.uk/424/

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