Optimally Protecting Elections with Uncertainty about Voter Preferences

Election control has always been an important issue of democratic institutions concerned. Considering that a voting rule is indeed susceptible to control by an external agent, it is natural to seek ways to protect elections. Much of prior work has focused on complete voter preferences and approached the problem from the perspective of the computational complexity of election control. However, it is impractical for everyone to have complete voter preferences in real-world scenarios. In addition, when given a voting rule, such as plurality which is widely used in our lives, is easy to control, how to design protection strategies to prevent the occurrence of election control is ignored. In this paper, we model the problem, where the attacker can deploy a single attack such as a denial-of-service attack to convert the voting result through deleting some voter groups, and the defender allocates the limited protection resources to prevent attacks on specific voter groups, as a Stackelberg game. Then we first use the minimax regret decision criterion for uncertainty about voter preferences in the game. We also propose heuristic algorithms to speed up computing minimax regret for the Stackelberg game. Finally, we conduct detailed experiments on both synthetic and real data, which show that our algorithms lead to much better solution quality than other algorithms in the literature.