用抽样方法估计选举的胜率
Estimating the Margin of Victory of an Election using Sampling
摘要：
选举的胜率是衡量选举结果是否稳健的有用指标。它也起着至关重要的作用，在选举后的审计，投票等各种算法的样本量确定在这项工作中，我们提出了有效的抽样为基础的算法，估计选举的胜利幅度。更正式地说，我们引入了\textsc{$(c, ε, δ)$--Margin of Victory}问题，其中给定$\mathcal{E}$对$n$选民的选举，目标是在$c MoV(\mathcal{E})+εn$的附加因子内估计$\mathcal{E}$的胜利$M(\mathcal{E})$的差距。我们研究了\textsc{$(c, ε, δ)$--Margin of Victory}问题，许多常用的投票规则，包括评分规则，批准，Bucklin，最大，和科普兰$^α.$我们观察到，即使是计算胜利的保证金的投票规则是NP-硬，可能存在有效的抽样为基础的算法，观察到的情况下，最大和科普兰$^α$投票规则。
英文摘要：
The margin of victory of an election is a useful measure to capture the robustness of an election outcome. It also plays a crucial role in determining the sample size of various algorithms in post election audit, polling etc. In this work, we present efficient sampling based algorithms for estimating the margin of victory of elections. More formally, we introduce the \textsc{$(c, ε, δ)$--Margin of Victory} problem, where given an election $\mathcal{E}$ on $n$ voters, the goal is to estimate the margin of victory $M(\mathcal{E})$ of $\mathcal{E}$ within an additive factor of $c MoV(\mathcal{E})+εn$. We study the \textsc{$(c, ε, δ)$--Margin of Victory} problem for many commonly used voting rules including scoring rules, approval, Bucklin, maximin, and Copeland$^α.$ We observe that even for the voting rules for which computing the margin of victory is NP-Hard, there may exist efficient sampling based algorithms, as observed in the cases of maximin and Copeland$^α$ voting rules.
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