Publication Type

Working Paper

Version

publishedVersion

Publication Date

12-2004

Abstract

LS Penrose’s limit theorem (PLT) – which is implicit in Penrose [5, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while existing voters retain their weights and the relative quota is pegged, then – under certain conditions – the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover [3] prove some special cases of PLT; and conjecture that the theorem holds, under rather general conditions, for large classes of weighted voting games, various values of the quota, and with respect to several measures of voting power. We use simulation to test this conjecture. It is corroborated w.r.t. the Penrose–Banzhaf index for a quota of 50% but not for other values; w.r.t. the Shapley–Shubik index the conjecture is corroborated for all values of the quota (short of 100%).

Keywords

limit theorems, majority games, simulation, weighted votinggames

Discipline

Econometrics | Economic Theory

Research Areas

International Economics

Volume

26-2004

First Page

1

Last Page

83

Publisher

SMU Economics and Statistics Working Paper Series, No. 26-2004

City or Country

Singapore

Copyright Owner and License

Authors

Comments

Published in Mathematical Social Sciences, 2006, 51 (1), 290-106. https://doi.org/10.1016/j.mathsocsci.2005.06.001

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