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：我们研究了在多种流行的基于批准的多人胜选投票规则下，若干操纵与控制问题的复杂性。具体而言，我们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投票法（ABCCV）、最小化最大遗憾批准投票（MAV）等。结果表明，除少数例外情况外，这些规则普遍能够抵御本文所审视的各类策略性行为。此外，我们还针对这些问题的若干自然参数获得了多项固定参数可追踪性结果，并为某些特例推导出了多项式时间算法。