小投票群体逆幂指数问题的启发式和精确解
Heuristic and exact solutions to the inverse power index problem for small voting bodies
摘要：
权力指数是量化投票机构成员对集体决策的影响的先验映射。它们的非线性和不连续性使得难以计算逆像，即，以确定引起尽可能接近期望的功率分布的表决系统。本文认为近似和精确解这个反问题的Penrose-Banzhaf指数，这是通过枚举和整数线性规划技术。他们进行了比较的结果，三个简单的解决方案quietistics。在绝对值方面，该算法表现良好，但在相对值方面可以大大改进。这一发现补充了大型投票机构的已知渐近结果，并可能改善局部搜索算法的终止标准。
英文摘要：
Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse images, i.e., to determine a voting system which induces a power distribution as close as possible to a desired one. This paper considers approximations and exact solutions to this inverse problem for the Penrose-Banzhaf index, which are obtained by enumeration and integer linear programming techniques. They are compared to the results of three simple solution heuristics. The heuristics perform well in absolute terms but can be improved upon very considerably in relative terms. The findings complement known asymptotic results for large voting bodies and may improve termination criteria for local search algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
