Much research in electoral control -- one of the most studied form of electoral attacks, in which an entity running an election alters the structure of that election to yield a preferred outcome -- has focused on giving decision complexity results, e.g., membership in P, NP-completeness, or fixed-parameter tractability. Approximability on the other hand has received little attention in electoral control, despite its prevalence in the study of other forms of electoral attacks, such as manipulation and bribery. Early work established preliminary results about popular voting rules such as plurality, approval, and Condorcet. In this paper, we completely determine for each of the "standard" control problems under plurality, approval, and Condorcet, whether they are approximable, and we prove our results in both the weighted and unweighted voter settings.

翻译：选举控制——一种被广泛研究的选举攻击形式，其中选举管理者通过改变选举结构以获得偏好的结果——已有大量研究关注决策复杂性结果，例如属于P类、NP完全性，或固定参数可解性。然而，近似性在选举控制中受到的关注甚少，尽管它在操纵和贿赂等其他形式的选举攻击研究中非常普遍。早期工作建立了关于多数投票、批准投票和孔多塞投票等常见投票规则的初步结果。在本文中，我们完整地确定了多数投票、批准投票和孔多塞投票规则下每个“标准”控制问题是否可近似，并在加权和未加权选民设置中证明了我们的结果。