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Often Harder than in the Constructive Case: Destructive Bribery in CP-nets

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Web and Internet Economics (WINE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9470))

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Abstract

We study the complexity of the destructive bribery problem (an external agent tries to prevent a disliked candidate from winning by bribery actions) in voting over combinatorial domains, where the set of candidates is the Cartesian product of several issues. This problem is related to the concept of the margin of victory of an election which constitutes a measure of robustness of the election outcome and plays an important role in the context of electronic voting. In our setting, voters have conditional preferences over assignments to these issues, modelled by CP-nets. We settle the complexity of all combinations of this problem based on distinctions of four voting rules, five cost schemes, three bribery actions, weighted and unweighted voters, as well as the negative and the non-negative scenario. We show that almost all of these cases are \(\mathcal {NP}\)-complete or \(\mathcal {NP}\)-hard for weighted votes while approximately half of the cases can be solved in polynomial time for unweighted votes.

P. Scharpfenecker—Supported by DFG grant TO 200/3-1.

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Notes

  1. 1.

    The formula given here differs from the one of Mattei et al. [19]. See the argument of Dorn and Krüger [7, Remark 1] why both are equivalent.

  2. 2.

    This is most unintuitive for \(C_\textsc {dist} \), but identifying the top candidate after bribing one issue and determining the respective cost can be done in polynomial time as described by Mattei et al. [19, Theorem 3].

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Science, University of Tübingen, Tübingen, Germany

    Britta Dorn

  2. Institute of Theoretical Computer Science, Ulm University, Ulm, Germany

    Dominikus Krüger & Patrick Scharpfenecker

Authors
  1. Britta Dorn
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  2. Dominikus Krüger
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  3. Patrick Scharpfenecker
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Correspondence to Britta Dorn .

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Editors and Affiliations

  1. Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis

  2. CWI and VU Amsterdam, Amsterdam, The Netherlands

    Guido Schäfer

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Dorn, B., Krüger, D., Scharpfenecker, P. (2015). Often Harder than in the Constructive Case: Destructive Bribery in CP-nets. In: Markakis, E., Schäfer, G. (eds) Web and Internet Economics. WINE 2015. Lecture Notes in Computer Science(), vol 9470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48995-6_23

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  • DOI: https://doi.org/10.1007/978-3-662-48995-6_23

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