International Conference on Algorithmic DecisionTheory

ADT 2015: Algorithmic Decision Theory pp 71-85 | Cite as

Manipulation of k-Approval in Nearly Single-Peaked Electorates

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9346)

Abstract

For agents it can be advantageous to vote insincerely in order to change the outcome of an election. This behavior is called manipulation. The Gibbard-Satterthwaite theorem states that in principle every non-trivial voting rule with at least three candidates is susceptible to manipulation. Since the seminal paper by Bartholdi, Tovey, and Trick in 1989, (coalitional) manipulation has been shown \(\mathrm{NP}\)-hard for many voting rules. However, under single-peaked preferences – one of the most influential domain restrictions – the complexity of manipulation often drops from \(\mathrm{NP}\)-hard to \(\mathrm{P}\).

In this paper, we investigate the complexity of manipulation for the k-approval and veto families of voting rules in nearly single-peaked elections, exploring the limits where the manipulation problem turns from \(\mathrm{P}\) to \(\mathrm{NP}\)-hard. Compared to the classical notion of single-peakedness, notions of nearly single-peakedness are more robust and thus more likely to appear in real-world data sets.

Notes

Acknowledgments

We thank the anonymous ADT-2015 referees for their very helpful comments and suggestions. This work was supported by the Austrian Science Fund (FWF): P25518, Y698, and the German Research Foundation (DFG): ER 738/2-1.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Economic DisciplinesUniversity of SiegenSiegenGermany
  2. 2.Institute of Information SystemsTU WienViennaAustria

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