The power of a collectivity to act in weighted voting games with many small voters
研究大型委员会在加权投票中通过随机提案的倾向，发现大量小投票者渐近地改变了大投票者之间的投票配额，并估计了收敛速度，对欧盟理事会决策规则有应用。
We analyze the propensity to approve a random proposal of a large committee that makes decisions by weighted voting. The approach is a generalized version of James Coleman’s “power of a collectivity to act”. Throughout the paper it is assumed that the voters are of two kinds: a fixed (possibly empty) set of “major” (big) voters with fixed weights, and an ever-increasing number of “minor” (small) voters, whose total weight is also fixed, but where each individual’s weight becomes negligible. As our main result, we obtain that asymptotically many minor voters act like a modification of the quota for the vote among major voters. The paper estimates the rate of convergence which turns out to be very high if the weight distribution among the small voters is not too skewed. The results obtained are illustrated by evaluating the decision rules for the Council of Ministers of the EU for various scenarios of EU enlargement.