论文标题
在Banzhaf和Shapley-Shubik固定点和Divisor投票系统上
On Banzhaf and Shapley-Shubik Fixed Points and Divisor Voting Systems
论文作者
论文摘要
Banzhaf和Shapley-Shubik Power指数首先是为了衡量选民在加权投票系统中的力量。鉴于加权投票系统，通过不断重新分配每个选民的权力指数，直到操作无法更改该系统，可以找到这种系统的固定点。我们表征了$ $ $（a，b，\ ldots，b）$的Shapley-Shubik功率指数下的所有固定点，并给出一个代数方程，可以原则上验证该表格是否为Banzhaf固定；我们还生成了$ $（a，a，b，\ ldots，b）$的Shapley-Shubik固定类。我们还研究了数量丰富的Divisor投票系统的指标，并证明Banzhaf和Shapley-Shubik指数在某些情况下有所不同。
The Banzhaf and Shapley-Shubik power indices were first introduced to measure the power of voters in a weighted voting system. Given a weighted voting system, the fixed point of such a system is found by continually reassigning each voter's weight with its power index until the system can no longer be changed by the operation. We characterize all fixed points under the Shapley-Shubik power index of the form $(a,b,\ldots,b)$ and give an algebraic equation which can verify in principle whether a point of this form is fixed for Banzhaf; we also generate Shapley-Shubik fixed classes of the form $(a,a,b,\ldots,b)$. We also investigate the indices of divisor voting systems of abundant numbers and prove that the Banzhaf and Shapley-Shubik indices differ for some cases.
