SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
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
On the parameterized complexity of some optimization problems related to multiple-interval graphs
Theoretical Computer Science
On problem kernels for possible winner determination under the k-approval protocol
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Approximation algorithms for campaign management
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Multimode control attacks on elections
Journal of Artificial Intelligence Research
Possible winners when new alternatives join: new results coming up!
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Computational complexity of two variants of the possible winner problem
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Winner determination in voting trees with incomplete preferences and weighted votes
Autonomous Agents and Multi-Agent Systems
On the evaluation of election outcomes under uncertainty
Artificial Intelligence
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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, if 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 and providing new many-one reductions, 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.