We study the parameterized complexity of Winners Determination for three prevalent -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 Winners Determination for these rules is NP-hard. Moreover, these problems have been studied from the parameterized complexity point of view with respect to some natural parameters recently. However, many results turned out to be W[1]-hard or W[2]-hard. Aiming at deriving more fixed-parameter algorithms, we revisit these problems by considering more natural and important single parameters, combined parameters, and structural parameters.
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