LS Penrose’s limit theorem: Tests by simulation

Pao-Li Chang (), Vincent CH Chua () and Moshé Machover
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Vincent CH Chua: School of Economics and Social Sciences, Singapore Management University

No 26-2004, Working Papers from Singapore Management University, School of Economics

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 voting games (search for similar items in EconPapers)
JEL-codes: C71 D71 (search for similar items in EconPapers)
Pages: 84 pages
Date: 2004-07
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Citations: View citations in EconPapers (15)

Published in SMU Economics and Statistics Working Paper Series

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Journal Article: L S Penrose's limit theorem: Tests by simulation (2006)
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