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We study the problem of bribery in multiwinner elections, for the case wherethe voters cast approval ballots (i.e., sets of candidates they approve) andthe bribery actions are limited to: adding an approval to a vote, deleting anapproval from a vote, or moving an approval within a vote from one candidate tothe other. We consider a number of approval-based multiwinner rules (AV, SAV,GAV, RAV, approval-based Chamberlin--Courant, and PAV). We find the landscapeof complexity results quite rich, going from polynomial-time algorithms throughNP-hardness with constant-factor approximations, to outright inapproximability.Moreover, in general, our problems tend to be easier when we limit out briberyactions on increasing the number of approvals of the candidate that we want tobe in a winning committee (i.e., adding approvals only for this preferredcandidate, or moving approvals only to him or her). We also study parameterizedcomplexity of our problems, with a focus on parameterizations by the numbers ofvoters or candidates.

Bribery as a Measure of Candidate Success: Complexity Results for Approval-Based Multiwinner Rules