42 research outputs found
LS Penrose’s limit theorem: Tests by simulation
No full textLS 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
A Place for the Palestinians in the Altneuland: Herzl, Anti-Semitism, and the Jewish State
No full textCollective Decision-Making and Supervision in a Communist Society
No full textThis article brings together my commitment to communism and my scientific work in the theory of social choice, particularly the measurement of voting power. I have been composing it, on and off, for several years: writing a few paragraphs, then putting it aside and turning to more urgent current tasks. Originally I used the term ‘socialism ’ in the title and the body of the arti-cle; but I have now changed this to ‘communism’. Let me explain why. The terms ‘communist ’ and ‘communism ’ have undergone a significant semantic shift since the beginning of the 21st century. For long these terms had been usurped and virtually monopolized by Stalinized ‘official communism’. For this reason, anti-Stalinist communists tended to avoid these terms as self-description and a description of the kind of society they strive for. Instead, they used terms such as ‘revolutionary socialists ’ as self-description, and ‘so-cialism ’ for their aim. (The term ‘socialism ’ was also usurped by Stalinists, but they never managed to monopolize it.) However, with the collapse of ‘of-ficial communism’, there has been a growing tendency to reclaim the forme
L S Penrose's Limit Theorem: Tests by simulation
No full textL S Penrose’s Limit Theorem – which is implicit in Penrose [7, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely 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 [4] prove some special cases of Penrose’s Limit Theorem. They give a simple counter-example showing that the theorem does not hold in general even under the conditions assumed by Penrose; but they conjecture, in effect, that under rather general conditions it holds ‘almost always’ – that is with probability 1 – for large classes of weighted voting games, for various values of the quota, and with respect to several measures of voting power. We use simulation to test this conjecture. It is corroborated with respect to the Penrose–Banzhaf index for a quota of 50% but not for other values; with respect to the Shapley–Shubik index the conjecture is corroborated for all values of the quota (short of 100%)
L S Penrose's Limit Theorem: Tests by Simulation
No full textPublished in Mathematical Social Sciences, 2006, 51 (1), 290-106. https://doi.org/10.1016/j.mathsocsci.2005.06.001</p
