Parameterized Computational Complexity of Dodgson and Young Elections

  • Nadja Betzler
  • Jiong Guo
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)


We show that, other than for standard complexity theory with known NP-completeness results, the computational complexity of the Dodgson and Young election systems is completely different from a parameterized complexity point of view. That is, on the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]-complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixed-parameter tractability as well as W[2]-hardness results depending on the cost model for switching ties.


Social Choice Election System Condorcet Winner Editing Operation Preference List 
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.A., Trick, M.A.: Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare 6, 157–165 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Betzler, N., Fellows, M.R., Guo, J., Niedermeier, R., Rosamond, F.A.: Fixed-parameter algorithms for Kemeny scores. In: Proc. of 4th AAIM. LNCS, vol. 5034, pp. 60–71. Springer, Heidelberg (2008)Google Scholar
  3. 3.
    Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A short introduction to computational social choice (invited paper). In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 51–69. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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
  6. 6.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  7. 7.
    Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: A richer understanding of the complexity of election systems. In: Ravi, S., Shukla, S. (eds.) Fundamental Problems in Computing: Essays in Honor of Professor Daniel J. Rosenkrantz. Springer, Heidelberg (2008)Google Scholar
  8. 8.
    Fellows, M.R.: Personal communication (October 2007)Google Scholar
  9. 9.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)Google Scholar
  10. 10.
    Hemaspaandra, E., Hemaspaandra, L.A.: Dichotomy for voting systems. Journal of Computer and System Sciences 73(1), 73–83 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Exact analysis of Dodgson elections: Lewis Caroll’s 1876 voting system is complete for parallel access to NP. Journal of the ACM 44(6), 806–825 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Homan, C.M., Hemaspaandra, L.A.: Guarantees for the success frequency of an algorithm for finding Dodgson-election winners. Journal of Heuristics (2007)Google Scholar
  13. 13.
    McCabe-Dansted, J.C.: Approximability and computational feasibility of Dodgson’s rule. Master’s thesis, University of Auckland (2006)Google Scholar
  14. 14.
    McCabe-Dansted, J.C., Pritchard, G., Slinko, A.: Approximability of Dodgson’s rule. Social Choice and Welfare (2007)Google Scholar
  15. 15.
    McLean, I., Urken, A.: Classics of Social Choice. University of Michigan Press, Ann Arbor, Michigan (1995)Google Scholar
  16. 16.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)zbMATHGoogle Scholar
  17. 17.
    Procaccia, A.D., Feldman, M., Rosenschein, J.S.: Approximability and inapproximability of Dodgson and Young elections. Technical Report Discussion paper 466, Center for the Study of Rationality, Hebrew University (October 2007)Google Scholar
  18. 18.
    Rothe, J., Spakowski, H., Vogel, J.: Exact complexity of the winner problem for Young elections. Theory of Computing Systems 36, 375–386 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Young, H.P.: Extending Condorcet’s rule. Journal of Economic Theory 16, 335–353 (1977)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nadja Betzler
    • 1
  • Jiong Guo
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations