English, Article, Journal or magazine article edition: LS Penrose’s limit theorem: Tests by simulation Pao-Li Chang; Vincent CH Chua; Moshe Machover

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Bookmark: http://trove.nla.gov.au/version/6166
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • LS Penrose’s limit theorem: Tests by simulation
Author
  • Pao-Li Chang
  • Vincent CH Chua
  • Moshe Machover
Physical Description
  • preprint
Notes
  • 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%).
  • limit theorems, majority games, simulation, weighted voting games
  • RePEc:siu:wpaper:26-2004
Language
  • English
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