Optimally Protecting Elections

Election control encompasses attempts from an external agent to alter the structure of an election in order to change its outcome. This problem is both a fundamental theoretical problem in social choice, and a major practical concern for democratic institutions. Consequently, this issue has received considerable attention, particularly as it pertains to different voting rules. In contrast, the problem of how election control can be prevented or deterred has been largely ignored. We introduce the problem of optimal protection against election control, where manipulation is allowed at the granularity of groups of voters (e.g., voting locations), through a denial-of-service attack, and the defender allocates limited protection resources to prevent control. We show that for plurality voting, election control through group deletion to prevent a candidate from winning is in P, while it is NP-Hard to prevent such control. We then present a double-oracle framework for computing an optimal prevention strategy, developing exact mixed-integer linear programming formulations for both the defender and attacker oracles (both of these subproblems we show to be NP-Hard), as well as heuristic oracles. Experiments conducted on both synthetic and real data demonstrate that the proposed computational framework can scale to realistic problem instances.