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Manipulation of k-Approval in Nearly Single-Peaked Electorates

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Book cover Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

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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.

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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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Authors and Affiliations

  1. School of Economic Disciplines, University of Siegen, Siegen, Germany

    Gábor Erdélyi & Andreas Pfandler

  2. Institute of Information Systems, TU Wien, Vienna, Austria

    Martin Lackner & Andreas Pfandler

Authors
  1. Gábor Erdélyi
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  2. Martin Lackner
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  3. Andreas Pfandler
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Corresponding authors

Correspondence to Gábor Erdélyi , Martin Lackner or Andreas Pfandler .

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Editors and Affiliations

  1. University of New South Wales, Kensington, Australia

    Toby Walsh

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Erdélyi, G., Lackner, M., Pfandler, A. (2015). Manipulation of k-Approval in Nearly Single-Peaked Electorates. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23113-6

  • Online ISBN: 978-3-319-23114-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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