L S Penrose's limit theorem: Tests by simulation
AbstractLS Penroseâs limit theorem (PLT) â which is implicit in Penrose [5, p. 72] and for which he gave no rigorous proof â 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 â under certain conditions â the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover  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 PenroseâBanzhaf index for a quota of 50% but not for other values; w.r.t. the ShapleyâShubik index the conjecture is corroborated for all values of the quota (short of 100%).
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 51 (2006)
Issue (Month): 1 (January)
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Web page: http://www.elsevier.com/locate/inca/505565
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- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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- Lindner, Ines & Machover, Moshe, 2004. "L.S. Penrose's limit theorem: proof of some special cases," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 37-49, January.
- Le Breton, Michel & Lepelley, Dominique, 2012.
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- Dennis Leech, 2013. "Power indices in large voting bodies," Public Choice, Springer, vol. 155(1), pages 61-79, April.
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