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L.S. Penrose's limit theorem: proof of some special cases

By I. Lindner and M. Machover


L.S. Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf (Bz) index’). His limit theorem—which is implicit in his booklet (1952) and for which he gave no rigorous proof—says that in simple weighted voting games (WVGs), if the number of voters increases indefinitely while the quota is pegged at half the total weight, then—under certain conditions—the ratio between the voting powers (as measured by him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined WVGs, other values of the quota, and other measures of voting power. We provide proofs for some special cases

Topics: Limit theorems, Majority games, Ternary weighted games, Weighted voting games, C71, D71
Publisher: Elsevier
Year: 2004
OAI identifier:
Provided by: DSpace at VU

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