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International Computer Science Symposium in Russia

CSR 2020: Computer Science – Theory and Applications pp 314–327Cite as

The Complexity of Controlling Condorcet, Fallback, and k-Veto Elections by Replacing Candidates or Voters

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12159))

Abstract

Electoral control models malicious ways of tampering with the outcome of elections via structural changes and has turned out to be one of the central themes in computational social choice. While the standard control types—adding/deleting/partitioning either voters or candidates—have been studied quite comprehensively, much less is known for the control actions of replacing voters or candidates. Continuing the work of Loreggia et al. [18, 19] and Erdélyi, Reger, and Yang [10], we study the computational complexity of control by replacing candidates or voters in Condorcet, fallback, and k-veto elections.

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Notes

  1. 1.

    One minor difference is that while Erdélyi et al. [10] show that k-veto is resistant to constructive control by replacing voters for \(k \ge 3\) (with vulnerability holding for \(k \le 2\)), Lin [16, 17] shows that it is resistant to constructive control by deleting voters for \(k \ge 4\) (with vulnerability holding for \(k \le 3\)).

References

  1. Bartholdi III, J., Tovey, C., Trick, M.: How hard is it to control an election? Math. Comput. Modell. 16(8/9), 27–40 (1992)

    Article  MathSciNet  Google Scholar 

  2. Baumeister, D., Erdélyi, G., Erdélyi, O., Rothe, J.: Control in judgment aggregation. In: Proceedings of the 6th European Starting AI Researcher Symposium, pp. 23–34. IOS Press, August 2012

    Google Scholar 

  3. Baumeister, D., Rothe, J.: Preference aggregation by voting. In: Rothe, J. (ed.) Economics and Computation. STBE, pp. 197–325. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-47904-9_4

    Chapter  Google Scholar 

  4. Baumeister, D., Rothe, J., Selker, A.-K.: Complexity of bribery and control for uniform premise-based quota rules under various preference types. In: Walsh, T. (ed.) ADT 2015. LNCS (LNAI), vol. 9346, pp. 432–448. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23114-3_26

    Chapter  Google Scholar 

  5. Brams, S., Sanver, R.: Voting systems that combine approval and preference. In: Brams, S., Gehrlein, W., Roberts, F. (eds.) The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn. Studies in Choice and Welfare, pp. 215–237. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-79128-7_12

    Chapter  Google Scholar 

  6. Chen, J., Faliszewski, P., Niedermeier, R., Talmon, N.: Elections with few voters: candidate control can be easy. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, pp. 2045–2051. AAAI Press (Jan 2015)

    Google Scholar 

  7. Erdélyi, G., Fellows, M., Rothe, J., Schend, L.: Control complexity in Bucklin and fallback voting: a theoretical analysis. J. Comput. Syst. Sci. 81(4), 632–660 (2015)

    Article  MathSciNet  Google Scholar 

  8. Erdélyi, G., Fellows, M., Rothe, J., Schend, L.: Control complexity in Bucklin and fallback voting: an experimental analysis. J. Comput. Syst. Sci. 81(4), 661–670 (2015)

    Article  MathSciNet  Google Scholar 

  9. Erdélyi, G., Piras, L., Rothe, J.: The complexity of voter partition in Bucklin and fallback voting: solving three open problems. In: Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems, IFAAMAS, pp. 837–844, May 2011

    Google Scholar 

  10. Erdélyi, G., Reger, C., Yang, Y.: Towards completing the puzzle: solving open problems for control in elections. In: Proceedings of the 18th International Conference on Autonomous Agents and Multiagent Systems, IFAAMAS, pp. 846–854, May 2019

    Google Scholar 

  11. Erdélyi, G., Rothe, J.: Control complexity in fallback voting. In: Proceedings of Computing: the 16th Australasian Theory Symposium, Australian Computer Society Conferences in Research and Practice in Information Technology Series, vol. 32, no. 8, pp. 39–48, January 2010

    Google Scholar 

  12. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: Multimode control attacks on elections. J. Artif. Intell. Res. 40, 305–351 (2011)

    Article  MathSciNet  Google Scholar 

  13. Faliszewski, P., Rothe, J.: Control and bribery in voting. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A. (eds.) Handbook of Computational Social Choice, chap. 7, pp. 146–168. Cambridge University Press (2016)

    Google Scholar 

  14. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H Freeman and Company, New York (1979)

    MATH  Google Scholar 

  15. Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Anyone but him: the complexity of precluding an alternative. Artif. Intell. 171(5–6), 255–285 (2007)

    Article  MathSciNet  Google Scholar 

  16. Lin, A.: The complexity of manipulating \(k\)-approval elections. In: Proceedings of the 3rd International Conference on Agents and Artificial Intelligence, pp. 212–218. SciTePress, January 2011

    Google Scholar 

  17. Lin, A.: Solving hard problems in election systems. Ph.D. thesis, Rochester Institute of Technology, Rochester, NY, USA, March 2012

    Google Scholar 

  18. Loreggia, A.: Iterative voting and multi-mode control in preference aggregation. Intelligenza Artificiale 8(1), 39–51 (2014)

    Article  Google Scholar 

  19. Loreggia, A., Narodytska, N., Rossi, F., Venable, B., Walsh, T.: Controlling elections by replacing candidates or votes (extended abstract). In: Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems, IFAAMAS, pp. 1737–1738, May 2015

    Google Scholar 

  20. Maushagen, C., Rothe, J.: Complexity of control by partitioning veto and maximin elections and of control by adding candidates to plurality elections. In: Proceedings of the 22nd European Conference on Artificial Intelligence, pp. 277–285. IOS Press, August/September 2016

    Google Scholar 

  21. Maushagen, C., Rothe, J.: Complexity of control by partition of voters and of voter groups in veto and other scoring protocols. In: Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems, IFAAMAS, pp. 615–623, May 2017

    Google Scholar 

  22. Maushagen, C., Rothe, J.: Complexity of control by partitioning veto elections and of control by adding candidates to plurality elections. Ann. Math. Artif. Intell. 82(4), 219–244 (2017). https://doi.org/10.1007/s10472-017-9565-7

    Article  MathSciNet  MATH  Google Scholar 

  23. Menton, C.: Normalized range voting broadly resists control. Theory Comput. Syst. 53(4), 507–531 (2013). https://doi.org/10.1007/s00224-012-9441-0

    Article  MathSciNet  MATH  Google Scholar 

  24. Rothe, J., Schend, L.: Challenges to complexity shields that are supposed to protect elections against manipulation and control: a survey. Ann. Math. Artif. Intell. 68(1–3), 161–193 (2013). https://doi.org/10.1007/s10472-013-9359-5

    Article  MathSciNet  MATH  Google Scholar 

  25. Walsh, T.: Is computational complexity a barrier to manipulation? Ann. Math. Artif. Intell. 62(1–2), 7–26 (2011). https://doi.org/10.1007/s10472-011-9255-9

    Article  MathSciNet  MATH  Google Scholar 

  26. Walsh, T.: Where are the hard manipulation problems? J. Artif. Intell. Res. 42, 1–29 (2011)

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

We thank the anonymous reviewers for their helpful comments. This work was supported in part by DFG grants RO-1202/14-2 and RO-1202/21-1.

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Authors and Affiliations

  1. Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

    Marc Neveling, Jörg Rothe & Roman Zorn

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  1. Marc Neveling
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  2. Jörg Rothe
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  3. Roman Zorn
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Correspondence to Jörg Rothe .

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  1. University of Trier, Trier, Germany

    Henning Fernau

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Neveling, M., Rothe, J., Zorn, R. (2020). The Complexity of Controlling Condorcet, Fallback, and k-Veto Elections by Replacing Candidates or Voters. In: Fernau, H. (eds) Computer Science – Theory and Applications. CSR 2020. Lecture Notes in Computer Science(), vol 12159. Springer, Cham. https://doi.org/10.1007/978-3-030-50026-9_23

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  • DOI: https://doi.org/10.1007/978-3-030-50026-9_23

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