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
When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
Universal voting protocol tweaks to make manipulation hard
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Social interaction under uncertainty in multi agent systems
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
Iterative voting under uncertainty for group recommender systems
Proceedings of the fourth ACM conference on Recommender systems
Determining possible and necessary winners under common voting rules given partial orders
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Winner determination in voting trees with incomplete preferences and weighted votes
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On the complexity of voting manipulation under randomized tie-breaking
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
Possible and necessary winners of partial tournaments
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
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We investigate the extent to which it is possible to evaluate 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 voters' preferences, but we know for each one the probability that it does. We give a polynomial algorithm to solve the problem of computing the probability that a given candidate will win when the number of candidates is a constant. However, when the number of candidates is not bounded, we prove that the problem becomes #P-Hard for the Plurality, Borda, and Copeland voting protocols. We further show that even evaluating if a candidate has any chance to win is NP-Complete for the Plurality voting protocol, in the weighted voters case. We give a polynomial algorithm for this problem when the voters' weights are equal.