Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
A sufficient condition for voting rules to be frequently manipulable
Proceedings of the 9th ACM conference on Electronic commerce
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Elections Can be Manipulated Often
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Junta distributions and the average-case complexity of manipulating elections
Journal of Artificial Intelligence Research
Universal voting protocol tweaks to make manipulation hard
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Where are the really hard manipulation problems? the phase transition in manipulating the veto rule
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Complexity of unweighted coalitional manipulation under some common voting rules
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A scheduling approach to coalitional manipulation
Proceedings of the 11th ACM conference on Electronic commerce
Equilibria of plurality voting with abstentions
Proceedings of the 11th ACM conference on Electronic commerce
The Geometry of Manipulation: A Quantitative Proof of the Gibbard-Satterthwaite Theorem
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Hybrid voting protocols and hardness of manipulation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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In their groundbreaking paper, Bartholdi, Tovey and Trick [1989] argued that many well-known voting rules, such as Plurality, Borda, Copeland and Maximin are easy to manipulate. An important assumption made in that paper is that the manipulator's goal is to ensure that his preferred candidate is among the candidates with the maximum score, or, equivalently, that ties are broken in favor of the manipulator's preferred candidate. In this paper, we examine the role of this assumption in the easiness results of [Bartholdi et al., 1989]. We observe that the algorithm presented in [Bartholdi et al., 1989] extends to all rules that break ties according to a fixed ordering over the candidates. We then show that all scoring rules are easy to manipulate if the winner is selected from all tied candidates uniformly at random. This result extends to Maximin under an additional assumption on the manipulator's utility function that is inspired by the original model of [Bartholdi et al., 1989]. In contrast, we show that manipulation becomes hard when arbitrary polynomial-time tie-breaking rules are allowed, both for the rules considered in [Bartholdi et al., 1989], and for a large class of scoring rules.