Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Journal of Computer and System Sciences
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
Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Uncertainty in preference elicitation and aggregation
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
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
Taking the Final Step to a Full Dichotomy of the Possible Winner Problem in Pure Scoring Rules
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Taking the final step to a full dichotomy of the possible winner problem in pure scoring rules
Information Processing Letters
Campaigns for lazy voters: truncated ballots
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Manipulation under voting rule uncertainty
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Control in the presence of manipulators: cooperative and competitive cases
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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A possible winner of an election is a candidate that has, in some kind of incomplete-information election, the possibility to win in a complete extension of the election. The first type of problem we study is the Possible co-Winner with respect to the Addition of New Candidates (PcWNA) problem, which asks, given an election with strict preferences over the candidates, is it possible to make a designated candidate win the election by adding a limited number of new candidates to the election? In the case of unweighted voters we show NP-completeness of PcWNA for a broad class of pure scoring rules. We will also briefly study the case of weighted voters. The second type of possible winner problem we study is Possible Winner/co-Winner under Uncertain Voting System (PWUVS and PcWUVS). Here, uncertainty is present not in the votes but in the election rule itself. For example, PcWUVS is the problem of whether, given a set C of candidates, a list of votes over C, a distinguished candidate c ∈ C, and a class of election rules, there is at least one election rule from this class under which c wins the election. We study these two problems for a class of systems based on approval voting, the family of Copelandα elections, and a certain class of scoring rules. Our main result is that it is NP-complete to determine whether there is a scoring vector that makes c win the election, if we restrict the set of possible scoring vectors for an m-candidate election to those of the form (α1,..., αm−4, x1, x2, x3, 0), with xi = 1 for at least one i ∈ {1, 2, 3}.