Journal of Computer and System Sciences
When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
Algorithms for the coalitional manipulation problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Nonexistence of voting rules that are usually hard to manipulate
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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
Hybrid voting protocols and hardness of manipulation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Frequent Manipulability of Elections: The Case of Two Voters
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Llull and Copeland voting computationally resist bribery and constructive control
Journal of Artificial Intelligence Research
How hard is bribery in elections?
Journal of Artificial Intelligence Research
Multimode control attacks on elections
IJCAI'09 Proceedings of the 21st international jont conference on Artifical 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
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
A scheduling approach to coalitional manipulation
Proceedings of the 11th ACM conference on Electronic commerce
Manipulation of copeland elections
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Using complexity to protect elections
Communications of the ACM
An Empirical Study of the Manipulability of Single Transferable Voting
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Comparing multiagent systems research in combinatorial auctions and voting
Annals of Mathematics and Artificial Intelligence
Is computational complexity a barrier to manipulation?
CLIMA'10 Proceedings of the 11th international conference on Computational logic in multi-agent systems
Information and Computation
Strategy-proof voting rules over multi-issue domains with restricted preferences
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Multimode control attacks on elections
Journal of Artificial Intelligence Research
Ties matter: complexity of voting manipulation revisited
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives
SIAM Journal on Computing
Is computational complexity a barrier to manipulation?
Annals of Mathematics and Artificial Intelligence
Where are the hard manipulation problems?
Journal of Artificial Intelligence Research
A quantitative gibbard-satterthwaite theorem without neutrality
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Ties matter: complexity of voting manipulation revisited
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Election manipulation: the average case
ACM SIGecom Exchanges
Discrete Applied Mathematics
Annals of Mathematics and Artificial Intelligence
A smooth transition from powerlessness to absolute power
Journal of Artificial Intelligence Research
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The Gibbard-Satterthwaite Theorem states that (in unrestricted settings) any reasonable voting rule is manipulable. Recently, a quantitative version of this theorem was proved by Ehud Friedgut, Gil Kalai, and Noam Nisan: when the number of alternatives is three, for any neutral voting rule that is far from any dictatorship, there exists a voter such that a random manipulation---that is, the true preferences and the strategic vote are all drawn i.i.d., uniformly at random---will succeed with a probability of Ω(1/n), where n is the number of voters. However, it seems that the techniques used to prove this theorem can not be fully extended to more than three alternatives. In this paper, we give a more limited result that does apply to four or more alternatives. We give a sufficient condition for a voting rule to be randomly manipulable with a probability of Ω(1/n) for at least one voter, when the number of alternatives is held fixed. Specifically, our theorem states that if a voting rule r satisfies 1. homogeneity, 2. anonymity, 3. non-imposition, 4. a canceling-out condition, and 5. there exists a stable profile that is still stable after one given alternative is uniformly moved to different positions; then there exists a voter such that a random manipulation for that voter will succeed with a probability of Ω(1/n). We show that many common voting rules satisfy these conditions, for example any positional scoring rule, Copeland, STV, maximin, and ranked pairs.