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
Citation
CHANG, Pao-Li; CHUA, Vincent; and MACHOVER, Moshe.
L S Penrose's Limit Theorem: Tests by Simulation. (2004). 26-2004, 1-83.
Available at: https://ink.library.smu.edu.sg/soe_research/827
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Comments
Published in Mathematical Social Sciences, 2006, 51 (1), 290-106. https://doi.org/10.1016/j.mathsocsci.2005.06.001