Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Complexity of manipulating elections with few candidates
Eighteenth national conference on Artificial intelligence
Vote elicitation: complexity and strategy-proofness
Eighteenth national conference on Artificial intelligence
When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
The computational complexity of choice sets
TARK '07 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge
Evaluation of election outcomes under uncertainty
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Complexity of terminating preference elicitation
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
On the complexity of schedule control problems for knockout tournaments
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
The learnability of voting rules
Artificial Intelligence
A new perspective on implementation by voting trees
Proceedings of the 10th ACM conference on Electronic commerce
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
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Llull and copeland voting broadly resist bribery and control
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Determining possible and necessary winners under common voting rules given partial orders
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Winner determination in sequential majority voting
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Incompleteness and incomparability in preference aggregation
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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
Towards a dichotomy for the Possible Winner problem in elections based on scoring rules
Journal of Computer and System Sciences
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
A new perspective on implementation by voting trees
Random Structures & Algorithms
Possible and necessary winners in voting trees: majority graphs vs. profiles
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Determining possible and necessary winners under common voting rules given partial orders
Journal of Artificial Intelligence Research
On the evaluation of election outcomes under uncertainty
Artificial Intelligence
Possible and necessary winners of partial tournaments
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
The complexity of losing voters
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
The complexity of online manipulation of sequential elections
Journal of Computer and System Sciences
Bribery in voting with CP-nets
Annals of Mathematics and Artificial Intelligence
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In multiagent settings where agents have different preferences, preference aggregation can be an important issue. Voting is a general method to aggregate preferences. We consider the use of voting tree rules to aggregate agents' preferences. In a voting tree, decisions are taken by performing a sequence of pairwise comparisons in a binary tree where each comparison is a majority vote among the agents. Incompleteness in the agents' preferences is common in many real-life settings due to privacy issues or an ongoing elicitation process. We study how to determine the winners when preferences may be incomplete, not only for voting tree rules (where the tree is assumed to be fixed), but also for the Schwartz rule (in which the winners are the candidates winning for at least one voting tree). In addition, we study how to determine the winners when only balanced trees are allowed. In each setting, we address the complexity of computing necessary (respectively, possible) winners, which are those candidates winning for all completions (respectively, at least one completion) of the incomplete profile. We show that many such winner determination problems are computationally intractable when the votes are weighted. However, in some cases, the exact complexity remains unknown. Since it is generally computationally difficult to find the exact set of winners for voting trees and the Schwartz rule, we propose several heuristics that find in polynomial time a superset of the possible winners and a subset of the necessary winners which are based on the completions of the (incomplete) majority graph built from the incomplete profiles.