Electoral control is the study of whether an attacker, by structural changes on an election such as adding/deleting/partitioning voters or candidates, can affect the winner in some desired way. Forty-four such attack types are often considered standard, and recently there has been work showing that sometimes the attack types -- though seemingly distinct -- in fact "collapse," that is, for every input, either the attacker can achieve their goal under both of the control types or under neither of the control types. The papers doing this, however, while often exploiting axiomatic results that ensured collapses, found all the separations by human or computer-generated counterexamples. This left open the issue of whether even the separation direction can be driven by axiomatic results that allow large groups of separations to be almost automatically obtained. Our paper provides many such results, and we apply them to seven important voting systems, finding sixty-four new collapses and 1901 new separations. We not only give axiomatic sufficient conditions and one complete characterization result, but also identify some control-problem pairs that universally separate -- in other words, they separate under every voting rule.

翻译：选举控制研究的是攻击者能否通过选举的结构性变化（如增加/删除/划分选民或候选人），以某种期望方式影响获胜者。通常有44种此类攻击类型被视为标准，近期研究表明，尽管这些攻击类型看似不同，但实际上有时会“坍缩”——即对每个输入而言，攻击者要么在两种控制类型下都能实现目标，要么都不能。然而，这些研究尽管常借助确保坍缩的公理结果，却通过人工或计算机生成的相反案例实现了所有分离现象。这便留下一个开放问题：分离方向本身能否由允许大规模分离近乎自动获取的公理结果所驱动？本文提供了大量此类结果，并将其应用于七个重要投票系统，发现了64个新坍缩和1901个新分离。我们不仅给出了公理充分条件及一个完整刻画结果，还识别出一些普遍分离的控制-问题对——换言之，这些对在所有投票规则下均能分离。