Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Vote elicitation: complexity and strategy-proofness
Eighteenth national conference on Artificial intelligence
Communication complexity of common voting rules
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Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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A Short Introduction to Computational Social Choice
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Algorithms for the coalitional manipulation problem
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On the parameterized complexity of multiple-interval graph problems
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Uncertainty in preference elicitation and aggregation
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Approximability of manipulating elections
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Determining possible and necessary winners under common voting rules given partial orders
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Winner determination in sequential majority voting
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Incompleteness and incomparability in preference aggregation
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Fixed-parameter algorithms for Kemeny rankings
Theoretical Computer Science
Llull and Copeland voting computationally resist bribery and constructive control
Journal of Artificial Intelligence Research
A multivariate complexity analysis of determining possible winners given incomplete votes
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
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Improved Parameterized Algorithms for the Kemeny Aggregation Problem
Parameterized and Exact Computation
A scheduling approach to coalitional manipulation
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Compilation and communication protocols for voting rules with a dynamic set of candidates
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
The nearest neighbor spearman footrule distance for bucket, interval, and partial orders
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Determining possible and necessary winners under common voting rules given partial orders
Journal of Artificial Intelligence Research
Taking the final step to a full dichotomy of the possible winner problem in pure scoring rules
Information Processing Letters
Winner determination in voting trees with incomplete preferences and weighted votes
Autonomous Agents and Multi-Agent Systems
Comparing and aggregating partial orders with kendall tau distances
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Cloning in elections: finding the possible winners
Journal of Artificial Intelligence Research
A maximum likelihood approach towards aggregating partial orders
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
On the evaluation of election outcomes under uncertainty
Artificial Intelligence
Campaigns for lazy voters: truncated ballots
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Possible and necessary winners of partial tournaments
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Voting with partial information: what questions to ask?
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
The nearest neighbor Spearman footrule distance for bucket, interval, and partial orders
Journal of Combinatorial Optimization
The complexity of online manipulation of sequential elections
Journal of Computer and System Sciences
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To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the Possible Winner problem that asks, given a set of partial votes, whether a distinguished candidate can still become a winner. In this work, we consider the computational complexity of Possible Winner for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, k-approval, and Borda. Generalizing previous NP-hardness results for some special cases, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that Possible Winner is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2,1,...,1,0), while it is solvable in polynomial time for plurality and veto.