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Ties matter: complexity of voting manipulation revisited
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Complexity of voting manipulation is a prominent research topic in computational social choice. In this paper, we study the complexity of optimal manipulation, i.e., finding a manipulative vote that achieves the manipulator's goal yet deviates as little as possible from her true ranking. We study this problem for three natural notions of closeness, namely, swap distance, footrule distance, and maximum displacement distance, and a variety of voting rules, such as scoring rules, Bucklin, Copeland, and Maximin. For all three distances, we obtain poly-time algorithms for all scoring rules and Bucklin and hardness results for Copeland and Maximin.