Unweighted coalitional manipulation under the Borda rule Is NP-hard

Authors:
Nadja Betzler;Rolf Niedermeier;Gerhard J. Woeginger
Affiliations:
TU Berlin, Berlin, Germany;TU Berlin, Berlin, Germany;TU Eindhoven, Eindhoven, The Netherlands
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Year:
2011

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Abstract

The Borda voting rule is a positional scoring rule where, for m candidates, for every vote the first candidate receives m- 1 points, the second m- 2 points and so on. A Borda winner is a candidate with highest total score. It has been a prominent open problem to determine the computational complexity of UNWEIGHTED COALITIONAL MANIPULATION UNDER BORDA: Can one add a certain number of additional votes (called manipulators) to an election such that a distinguished candidate becomes a winner? We settle this open problem by showing NP-hardness even for two manipulators and three input votes. Moreover, we discuss extensions and limitations of this hardness result.