Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
Computational aspects of preference aggregation
Computational aspects of preference aggregation
Evaluation of election outcomes under uncertainty
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 3
On the complexity of schedule control problems for knockout tournaments
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
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 broadly resist bribery and control
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Universal voting protocol tweaks to make manipulation hard
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A multivariate complexity analysis of determining possible winners given incomplete votes
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Compiling the votes of a subelectorate
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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
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
Incompleteness and incomparability in preference aggregation: Complexity results
Artificial Intelligence
Determining possible and necessary winners under common voting rules given partial orders
Journal of Artificial Intelligence Research
Winner determination in voting trees with incomplete preferences and weighted votes
Autonomous Agents and Multi-Agent Systems
A behavioral perspective on social choice
Annals of Mathematics and Artificial Intelligence
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We investigate the extent to which it is possible to compute the probability of a particular candidate winning an election, given imperfect information about the preferences of the electorate. We assume that for each voter, we have a probability distribution over a set of preference orderings. Thus, for each voter, we have a number of possible preference orderings - we do not know which of these orderings actually represents the preferences of the voter, but for each ordering, we know the probability that it does. For the case where the number of candidates is a constant, we are able to give a polynomial time algorithm to compute the probability that a given candidate will win. We present experimental results obtained with an implementation of the algorithm, illustrating how the algorithm@?s performance in practice is better than its predicted theoretical bound. However, when the number of candidates is not bounded, we prove that the problem becomes #P-hard for the Plurality, k-approval, Borda, Copeland, and Bucklin voting rules. We further show that even evaluating if a candidate has any chance of winning is NP-complete for the Plurality voting rule in the case where voters may have different weights. With unweighted voters, we give a polynomial algorithm for Plurality, and show that the problem is hard for many other voting rules. Finally, we give a Monte Carlo approximation algorithm for computing the probability of a candidate winning in any settings, with an error that is as small as desired.