Pao-Li Chang () (School of Economics and Social Sciences, Singapore Management University) Vincent CH Chua () (School of Economics and Social Sciences, Singapore Management University) Moshe Machover () (CPNSS LSE, London)
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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%).
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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number
26-2004.
Length: 84 pages Date of creation: Jul 2004 Date of revision: Publication status: Published in SMU Economics and Statistics Working Paper Series Handle: RePEc:siu:wpaper:26-2004
Find related papers by JEL classification: 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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