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Approval-like voting rules, such as Sincere-Strategy Preference-BasedApproval voting (SP-AV), the Bucklin rule (an adaptive variant of $k$-Approvalvoting), and the Fallback rule (an adaptive variant of SP-AV) have manydesirable properties: for example, they are easy to understand and encouragethe candidates to choose electoral platforms that have a broad appeal. In thispaper, we investigate both classic and parameterized computational complexityof electoral campaign management under such rules. We focus on two methods thatcan be used to promote a given candidate: asking voters to move this candidateupwards in their preference order or asking them to change the number ofcandidates they approve of. We show that finding an optimal campaign managementstrategy of the first type is easy for both Bucklin and Fallback. In contrast,the second method is computationally hard even if the degree to which we needto affect the votes is small. Nevertheless, we identify a large class ofscenarios that admit fixed-parameter tractable algorithms.

Campaign Management under Approval-Driven Voting Rules