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
How many candidates are needed to make elections hard to manipulate?
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Logical Preference Representation and Combinatorial Vote
Annals of Mathematics and Artificial Intelligence
Computational aspects of preference aggregation
Computational aspects of preference aggregation
Complexity of terminating preference elicitation
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Computing possible and necessary winners from incomplete partially-ordered preferences
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
mCP nets: representing and reasoning with preferences of multiple agents
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Nonexistence of voting rules that are usually hard to manipulate
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Incompleteness and incomparability in preference aggregation
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
On the evaluation of election outcomes under uncertainty
Artificial Intelligence
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
The complexity of losing voters
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Bribery in voting with CP-nets
Annals of Mathematics and Artificial Intelligence
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We consider how to combine the preferences of multiple agents despite the presence of incompleteness and incomparability in their preference relations over possible candidates. The set of preference relations of an agent may be incomplete because, for example, there is an ongoing preference elicitation process. There may also be incomparability as this is useful, for example, in multi-criteria scenarios. We focus here on the problem of computing the possible and necessary winners, that is, those candidates which can be, or always are, the most preferred for the agents. Possible and necessary winners are useful in many scenarios including preference elicitation. First, we show that testing possible and necessary winners is in general a computationally intractable problem for STV with unweighted votes and the cup rule with weighted votes, as is providing a good approximation of such sets. Then, we identify general properties of the preference aggregation function, such as independence to irrelevant alternatives, which are sufficient for such sets to be computed in polynomial time. Finally, we show how possible and necessary winners can be used to focus preference elicitation. We show that it is computationally intractable for the cup rule with weighted votes in the worst-case to decide when to terminate elicitation. However, we identify a property of the preference aggregation function that allows us to decide when to terminate elicitation in polynomial time, by focusing on possible and necessary winners.