On the Complexity of Destructive Bribery in Approval-Based Multi-winner Voting

Abstract

A variety of constructive manipulation, control, and bribery for approval-based multi-winner voting have been extensively studied very recently. However, their destructive counterparts seem to be less studied in the literature so far. This paper aims to fill this gap by exploring the complexity of several destructive bribery problems under five prestigious approval-based multi-winner voting rules. Generally speaking, these problems are to determine if a number of given candidates can be excluded from any winning committees by performing a series of modification operations yet without exceeding a given budget. We consider five operations. We offer a complete landscape of the complexity of the problems studied in this paper, and for NP-hard problems we study their parameterized complexity with respect to meaningful parameters.