Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
A sufficient condition for voting rules to be frequently manipulable
Proceedings of the 9th ACM conference on Electronic commerce
Elections Can be Manipulated Often
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Frequent Manipulability of Elections: The Case of Two Voters
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
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
A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives
SIAM Journal on Computing
On coalitions and stable winners in plurality
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Election manipulation: the average case
ACM SIGecom Exchanges
Normalized Range Voting Broadly Resists Control
Theory of Computing Systems
Annals of Mathematics and Artificial Intelligence
A smooth transition from powerlessness to absolute power
Journal of Artificial Intelligence Research
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Recently, quantitative versions of the Gibbard-Satterthwaite theorem were proven for k=3 alternatives by Friedgut, Kalai, Keller and Nisan and for neutral functions on k ≥ 4 alternatives by Isaksson, Kindler and Mossel. In the present paper we prove a quantitative version of the Gibbard-Satterthwaite theorem for general social choice functions for any number k ≥ 3 of alternatives. In particular we show that for a social choice function f on k ≥ 3 alternatives and n voters, which is ε-far from the family of nonmanipulable functions, a uniformly chosen voter profile is manipulable with probability at least inverse polynomial in n, k, and ε-1. Removing the neutrality assumption of previous theorems is important for multiple reasons. For one, it is known that there is a conflict between anonymity and neutrality, and since most common voting rules are anonymous, they cannot always be neutral. Second, virtual elections are used in many applications in artificial intelligence, where there are often restrictions on the outcome of the election, and so neutrality is not a natural assumption in these situations. Ours is a unified proof which in particular covers all previous cases established before. The proof crucially uses reverse hypercontractivity in addition to several ideas from the two previous proofs. Much of the work is devoted to understanding functions of a single voter, and in particular we also prove a quantitative Gibbard-Satterthwaite theorem for one voter.