Bribery as a Measure of Candidate Success: Complexity Results for Approval-Based Multiwinner Rules
This work addresses computational challenges in election manipulation for voting systems, providing insights into the robustness of multiwinner rules, but it is incremental as it extends existing bribery complexity studies to approval-based settings.
The paper investigates the computational complexity of bribery in multiwinner elections with approval ballots, analyzing various rules like AV, SAV, GAV, RAV, approval-based Chamberlin–Courant, and PAV, and finds a range of results from polynomial-time algorithms to NP-hardness and inapproximability, with easier cases when bribery actions are limited to increasing approvals for a preferred candidate.
We study the problem of bribery in multiwinner elections, for the case where the voters cast approval ballots (i.e., sets of candidates they approve) and the bribery actions are limited to: adding an approval to a vote, deleting an approval from a vote, or moving an approval within a vote from one candidate to the other. We consider a number of approval-based multiwinner rules (AV, SAV, GAV, RAV, approval-based Chamberlin--Courant, and PAV). We find the landscape of complexity results quite rich, going from polynomial-time algorithms through NP-hardness with constant-factor approximations, to outright inapproximability. Moreover, in general, our problems tend to be easier when we limit out bribery actions on increasing the number of approvals of the candidate that we want to be in a winning committee (i.e., adding approvals only for this preferred candidate, or moving approvals only to him or her). We also study parameterized complexity of our problems, with a focus on parameterizations by the numbers of voters or candidates.