必要的和可能的获胜者的数学技巧
Algorithmic Techniques for Necessary and Possible Winners
摘要：
我们调查的实际方面计算的必要和可能的赢家在选举中不完整的选民偏好。在必要的赢家的情况下，我们展示了如何实现和加速的多项式时间算法的夏和Conitzer。在可能的赢家的情况下，其中的问题是NP-难的，我们给一个自然的减少到所有的位置评分规则的线性规划（ILP），并实现它在一个领先的商业优化求解器。此外，我们设计的优化技术，以尽量减少ILP执行的数量，并经常完全避免它们。我们进行了彻底的实验研究，包括建设一个丰富的基准选举数据的基础上，真正的和合成数据。我们的研究结果表明，尽管最坏情况下的棘手的可能的赢家，这里提出的算法技术规模以及可用于计算可能的赢家在现实的情况下。
英文摘要：
We investigate the practical aspects of computing the necessary and possible winners in elections over incomplete voter preferences. In the case of the necessary winners, we show how to implement and accelerate the polynomial-time algorithm of Xia and Conitzer. In the case of the possible winners, where the problem is NP-hard, we give a natural reduction to Integer Linear Programming (ILP) for all positional scoring rules and implement it in a leading commercial optimization solver. Further, we devise optimization techniques to minimize the number of ILP executions and, oftentimes, avoid them altogether. We conduct a thorough experimental study that includes the construction of a rich benchmark of election data based on real and synthetic data. Our findings suggest that, the worst-case intractability of the possible winners notwithstanding, the algorithmic techniques presented here scale well and can be used to compute the possible winners in realistic scenarios.
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