委员会中权力分配的逆问题
The inverse problem for power distributions in committees
摘要：
在文献中已经引入了几个权力指数，以衡量个别委员会成员的影响力的汇总决定。在这里，我们提出了相反的问题，并旨在为委员会设计投票规则，以便尽可能接近地满足给定的期望权力分配。针对一类不同幂指数的整数线性规划问题，提出了一种精确算法。关于负近似结果，我们推广的方法阿隆和埃德尔曼谁研究的权力分布的Banzhaf指数，其中大部分的权力集中在几个坐标。事实证明，一个n人委员会的每个Banzhaf向量接近这样一个期望的权力分布，也必须接近一个k人委员会的Banzhaf向量。我们表明，这种阿隆-埃德尔曼型的结果是可能的其他权力指数，如公共利益指数或科尔曼指数，以防止行动，而他们主要是不可能的，例如约翰斯顿指数。
英文摘要：
Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We present an exact algorithm for a large class of different power indices based on integer linear programming. With respect to negative approximation results we generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, has to be also near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results are possible for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while they are principally impossible for e.g. the Johnston index.
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