A generalization of Condorcet’s Jury Theorem to weighted voting games with many small voters
将孔多塞陪审团定理推广到有两类投票者的加权投票游戏:固定权重的少数大投票者和总权重固定但个体权重可忽略的众多小投票者,得出陪审团正确决策的极限概率与少数大投票者能力的关系,并发现配额q=1/2起关键作用。
We extend Condorcet’s Jury Theorem (Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. De l’imprimerie royale, 1785) to weighted voting games with voters of two kinds: a fixed (possibly empty) set of ‘major’ voters with fixed weights, and an ever-increasing number of ‘minor’ voters, whose total weight is also fixed, but where each individual’s weight becomes negligible. As our main result, we obtain the limiting probability that the jury will arrive at the correct decision as a function of the competence of the few major players. As in Condorcet’s result the quota q = 1/2 is found to play a prominent role.