Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
Complexity of unweighted coalitional manipulation under some common voting rules
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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
Control complexity of schulze voting
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Schulze's rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which it satisfies. We identify a potential shortcoming of Schulze's rule: it is computationally vulnerable to manipulation. In particular, we prove that computing an unweighted coalitional manipulation (UCM) is polynomial for any number of manipulators. This result holds for both the unique winner and the co-winner versions of UCM. This resolves an open question in [14]. We also prove that computing a weighted coalitional manipulation (WCM) is polynomial for a bounded number of candidates. Finally, we discuss the relation between the unique winner UCM problem and the co-winner UCM problem and argue that they have substantially different necessary and sufficient conditions for the existence of a successful manipulation.