When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
Anyone but him: The complexity of precluding an alternative
Artificial Intelligence
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
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
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
Using complexity to protect elections
Communications of the ACM
Control complexity in fallback voting
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Multimode control attacks on elections
Journal of Artificial Intelligence Research
Possible winners when new alternatives join: new results coming up!
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
The complexity of voter partition in Bucklin and fallback voting: solving three open problems
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Computational complexity of two variants of the possible winner problem
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
How hard is it to control an election?
Mathematical and Computer Modelling: An International Journal
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Control and manipulation are two of the most studied types of attacks on elections. In this paper, we study the complexity of control attacks on elections in which there are manipulators. We study both the case where the "chair" who is seeking to control the election is allied with the manipulators, and the case where the manipulators seek to thwart the chair. In the latter case, we see that the order of play substantially influences the complexity. We prove upper bounds, holding over every election system with a polynomial-time winner problem, for all standard control cases, and some of these bounds are at the second or third level of the polynomial hierarchy, and we provide matching lower bounds to prove these tight. Nonetheless, for important natural systems the complexity can be much lower. We prove that for approval and plurality elections, the complexity of even competitive clashes between a controller and manipulators falls far below those high bounds, even as low as polynomial time. Yet we for a Borda-voting case show that such clashes raise the complexity unless NP = coNP.