Unweighted Coalitional Manipulation under the Borda Rule Is NP-Hard

@inproceedings{Betzler2011UnweightedCM,
  title={Unweighted Coalitional Manipulation under the Borda Rule Is NP-Hard},
  author={Nadja Betzler and Rolf Niedermeier and Gerhard J. Woeginger},
  booktitle={IJCAI},
  year={2011}
}
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… 
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Taking the final step to a full dichotomy of the possible winner problem in pure scoring rules
Where are the hard manipulation problems?
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  • Computer Science, Economics
    J. Artif. Intell. Res.
  • 2011
TLDR
Empirical studies are shown to be useful in improving the understanding of computational complexity in voting and manipulation, and two settings are considered which represent the two types of complexity results: manipulation with unweighted votes by a single agent, and manipulation with weighted Votes by a coalition of agents.
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References

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