On the Complexity of Voting Manipulation under Randomized Tie-Breaking
Svetlana Obraztsova and Edith Elkind
Computational complexity of voting manipulation is one of the most actively studied topics in the area of computational social choice, starting with the groundbreaking work of Bartholdi et al. (1989). Most of the existing work in this area, including that of Bartholdi et al., implicitly assumes that whenever several candidates receive the top score with respect to the given voting rule, the resulting tie is broken according to a lexicographic ordering over the candidates. However, till recently, an equally appealing method of tie-breaking, namely, selecting the winner uniformly at random among all tied candidates, has not been considered in the computational social choice literature. The first paper to analyze the complexity of voting manipulation under randomized tie-breaking is Obraztsova et al. (2011), where the authors provide polynomial-time algorithms for this problem under scoring rules and---under an additional assumption on manipulator's utilities---for Maximin. In this paper, we extend the results of Obraztsova et al. by showing that finding an optimal vote under randomized tie-breaking is computationally hard for Copeland and Maximin (with general utilities), as well as for STV and Ranked Pairs, but easy for the Bucklin rule and Plurality with Runoff.