Approximation Algorithms for Campaign Management

  • Edith Elkind
  • Piotr Faliszewski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6484)


We study electoral campaign management scenarios in which an external party can buy votes, i.e., pay the voters to promote its preferred candidate in their preference rankings. The external party’s goal is to make its preferred candidate a winner while paying as little as possible. We describe a 2-approximation algorithm for this problem for a large class of electoral systems known as scoring rules. Our result holds even for weighted voters, and has applications for campaign management in commercial settings. We also give approximation algorithms for our problem for two Condorcet-consistent rules, namely, the Copeland rule and maximin.


Approximation Algorithm Vote Rule Weighted Voter Condorcet Winner Prefer Candidate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bartholdi III, J., Tovey, C., Trick, M.: Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare 6(2), 157–165 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Betzler, N., Dorn, B.: Towards a dichotomy of finding possible winners in elections based on scoring rules. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 124–136. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Caragiannis, I., Covey, J., Feldman, M., Homan, C., Kaklamanis, C., Karanikolas, N., Procaccia, A., Rosenschein, J.: On the approximability of Dodgson and Young elections. In: Proceedings of SODA 2009, pp. 1058–1067 (January 2009)Google Scholar
  4. 4.
    Dorn, B., Schlotter, I.: Multivariate complexity analysis of swap bribery. In: Proceedings of the 5th International Symposium on Parameterized and Exact Computation (to appear, 2010)Google Scholar
  5. 5.
    Elkind, E., Faliszewski, P.: Approximation algorithms for campaign management. Tech. Rep. arXiv:1004.0334 [cs.GT] (March 2010)Google Scholar
  6. 6.
    Elkind, E., Faliszewski, P., Slinko, A.: Swap bribery. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) Algorithmic Game Theory. LNCS, vol. 5814, pp. 299–310. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Faliszewski, P.: Nonuniform bribery (short paper). In: Proceedings of AAMAS 2008, pp. 1569–1572 (2008)Google Scholar
  8. 8.
    Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: How hard is bribery in elections? Journal of Artificial Intelligence Research 35, 485–532 (2009)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Llull and Copeland voting computationally resist bribery and constructive control. Journal of Artificial Intelligence Research 35, 275–341 (2009)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Exact analysis of Dodgson elections: Lewis Carroll’s 1876 voting system is complete for parallel access to NP. Journal of the ACM 44(6), 806–825 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and sub-constant error-probability PCP characterization of NP. In: Proceedings of STOC 1997, pp. 475–484. ACM Press, New York (1997)Google Scholar
  12. 12.
    Xia, L., Conitzer, V.: Determining possible and necessary winners under common voting rules given partial orders. In: Proceedings of AAAI 2008, pp. 196–201 (July 2008)Google Scholar
  13. 13.
    Xia, L., Conitzer, V., Procaccia, A.: A scheduling approach to coalitional manipulation. In: Proceedings of EC 2010, pp. 275–284 (June 2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Edith Elkind
    • 1
  • Piotr Faliszewski
    • 2
  1. 1.School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore
  2. 2.Department of Computer ScienceAGH Univ. of Sci. and Tech.KrakówPoland

Personalised recommendations