Over the past few years, the (parameterized) complexity landscape of constructive control for many prevalent approval-based multiwinner voting (ABMV) rules has been explored. We expand these results in two directions. First, we study constructive control for sequential Thiele's rules. Second, we study destructive counterparts of these problems. Our exploration leads to a comprehensive understanding of the complexity of these problems. Along the way, we also study several interesting axiomatic properties of ABMV rules, and obtain generic results for rules fulfilling these properties. In particular, we show that for many rules satisfying these properties, election control problems are generally hard to solve from a parameterized complexity point of view, even when restricted to certain special cases.

翻译：过去数年，学者们已深入探索了多种主流批准制多赢家投票规则下建构性控制的（参数）复杂性景观。我们沿两个方向拓展了这些成果：首先，研究了序贯蒂勒规则的建构性控制问题；其次，探讨了此类问题的破坏性对应版本。通过系统研究，我们全面掌握了这些问题的复杂性本质。在研究过程中，我们还考察了批准制多赢家投票规则的若干重要公理性质，并针对满足这些性质的规则获得了通用性结论。特别地，研究表明：对于满足这些公理的多数规则而言，选举控制问题即使局限于特定特例情形，从参数复杂性视角看通常仍难以求解。