The interface between P and NP: COL, XOR, NAE, 1-in-k, and Horn SAT
Eighteenth national conference on Artificial intelligence
Threshold phenomena in random graph colouring and satisfiability
Threshold phenomena in random graph colouring and satisfiability
When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
Average-case tractability of manipulation in voting via the fraction of manipulators
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
A sufficient condition for voting rules to be frequently manipulable
Proceedings of the 9th ACM conference on Electronic commerce
Generalized scoring rules and the frequency of coalitional manipulability
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
Algorithms for the coalitional manipulation problem
Artificial Intelligence
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
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Llull and Copeland voting computationally resist bribery and constructive control
Journal of Artificial Intelligence Research
Finite local consistency characterizes generalized scoring rules
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
Voting almost maximizes social welfare despite limited communication
Artificial Intelligence
A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives
SIAM Journal on Computing
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
Computing the margin of victory for various voting rules
Proceedings of the 13th ACM Conference on Electronic Commerce
Unweighted coalitional manipulation under the Borda rule Is NP-hard
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
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We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is o (√n), where n is the number of voters, then the probability that a random profile is manipulable by the coalition goes to zero as the number of voters goes to infinity, whereas if the number of manipulators is ω(√n), then the probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size c√n, and we show that as c goes from zero to infinity, the limiting probability that a random profile is manipulable goes from zero to one in a smooth fashion, i.e., there is a smooth phase transition between the two regimes. This result analytically validates recent empirical results, and suggests that deciding the coalitional manipulation problem may be of limited computational hardness in practice.