We study the parameterized complexity of winner determination problems for three prevalent $k$-committee selection rules, namely the minimax approval voting (MAV), the proportional approval voting (PAV), and the Chamberlin-Courant's approval voting (CCAV). It is known that these problems are computationally hard. Although they have been studied from the parameterized complexity point of view with respect to several natural parameters, many of them turned out to be W[1]-hard or W[2]-hard. Aiming at obtaining plentiful fixed-parameter algorithms, we revisit these problems by considering more natural single parameters, combined parameters, and structural parameters.

翻译：我们研究了三种主流$k$-委员会选举规则中的胜者确定问题的参数化复杂度，即最小最大赞成票投票（MAV）、比例赞成票投票（PAV）和钱伯林-库朗赞成票投票（CCAV）。已知这些问题在计算上是困难的。尽管已从参数化复杂度角度针对若干自然参数进行了研究，但许多问题被证明属于W[1]-难或W[2]-难。为获得丰富的固定参数算法，我们通过考虑更自然的单个参数、组合参数和结构参数重新审视这些问题。