We investigate the complexity of several manipulation and control problems under numerous prevalent approval-based multiwinner voting rules. Particularly, the rules we study include approval voting (AV), satisfaction approval voting (SAV), net-satisfaction approval voting (NSAV), proportional approval voting (PAV), approval-based Chamberlin-Courant voting (ABCCV), minimax approval voting (MAV), etc. We show that these rules generally resist the strategic types scrutinized in the paper, with only a few exceptions. In addition, we also obtain many fixed-parameter tractability results for these problems with respect to several natural parameters, and derive polynomial-time algorithms for certain special cases.

翻译：本文研究了多种主流批准制多赢选举规则下若干操纵与控制问题的计算复杂性。具体考察的规则包括：批准投票（AV）、满意度批准投票（SAV）、净满意度批准投票（NSAV）、比例批准投票（PAV）、基于批准的Chamberlin-Courant投票（ABCCV）、最小最大批准投票（MAV）等。研究表明，除少数特例外，这些规则普遍对文中分析的策略性操控具有抗性。此外，针对若干自然参数，我们还获得了这些问题的多类固定参数可解性结果，并推导出特定情况下的多项式时间算法。