Parameterized Complexity of Candidate Control in Elections and Related Digraph Problems

  • Nadja Betzler
  • Johannes Uhlmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5165)

Abstract

There are different ways for an external agent to influence the outcome of an election. We concentrate on “control” by adding or deleting candidates of an election. Our main focus is to investigate the parameterized complexity of various control problems for different voting systems. To this end, we introduce natural digraph problems that may be of independent interest. They help in determining the parameterized complexity of control for different voting systems including Llull, Copeland, and plurality votings. Devising several parameterized reductions, we provide a parameterized complexity overview of the digraph and control problems with respect to natural parameters.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bartholdi III, J.J., Tovey, C.A., Trick, M.A.: How hard is it to control an election. Mathematical and Computer Modelling 16(8-9), 27–40 (1992)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Christian, R., Fellows, M.R., Rosamond, F.A., Slinko, A.M.: On complexity of lobbying in multiple referenda. Review of Economic Design 11(3), 217–224 (2007)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Conitzer, V., Sandholm, T., Lang, J.: When are elections with few candidates hard to manipulate? Journal of the ACM 54(3), 1–33 (2007)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Downey, R.G., Fellows, M.R.: Threshold dominating sets and an improved version of W[2]. Theoretical Computer Science 209, 123–140 (1998)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  6. 6.
    Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Llull and Copeland voting broadly resist bribery and control. In: Proc. of 22nd AAAI 2007, pp. 724–730 (2007)Google Scholar
  7. 7.
    Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Copeland voting fully resists constructive control. In: Proc. of 4th AAIM 2008 (2008)Google Scholar
  8. 8.
    Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Anyone but him: The complexity of precluding an alternative. Artificial Intelligence 171, 255–285 (2007)CrossRefMathSciNetGoogle Scholar
  9. 9.
    König, D.: Über Graphen und ihre Anwendungen auf Determinantentheorie und Mengenlehre. Mathematische Annalen 77, 453–465 (1916)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nadja Betzler
    • 1
  • Johannes Uhlmann
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations