Manipulating Stochastically Generated Single-Elimination Tournaments for Nearly All Players

  • Isabelle Stanton
  • Virginia Vassilevska Williams
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)


We study the power of a tournament organizer in manipulating the outcome of a balanced single-elimination tournament by fixing the initial seeding. This problem is known as agenda control for balanced voting trees. It is not known whether there is a polynomial time algorithm that computes a seeding for which a given player can win the tournament, even if the match outcomes for all pairwise player match-ups are known in advance. We approach the problem by giving a sufficient condition under which the organizer can always efficiently find a tournament seeding for which the given player will win the tournament. We then use this result to show that for most match outcomes generated by a natural random model attributed to Condorcet, the tournament organizer can very efficiently make a large constant fraction of the players win, by manipulating the initial seeding.


Match Outcome Social Choice Theory Strong Player Computational Social Choice Vote Tree 
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.


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  1. 1.
    Bartholdi, J., Tovey, C., Trick, M.: The computational difficulty of manipulating an election. Social Choice Welfare 6(3), 227–241 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bartholdi, J., Tovey, C., Trick, M.: How hard is it to control an election. Mathematical and Computer Modeling, 27–40 (1992)Google Scholar
  3. 3.
    Braverman, M., Mossel, E.: Noisy sorting without resampling. In: SODA, pp. 268–276 (2008)Google Scholar
  4. 4.
    Coppersmith, D., Fleischer, L., Rudra, A.: Ordering by weighted number of wins gives a good ranking for weighted tournaments. In: SODA, pp. 776–782 (2006)Google Scholar
  5. 5.
    Erdős, P., Rényi, A.: On random matrices. Publications of the Mathematical Institute Hungarian Academy of Science 8, 455–561 (1964)zbMATHGoogle Scholar
  6. 6.
    Feige, U., Peleg, D., Laghavan, P., Upfal, E.: Computing with unreliable information. In: STOC, pp. 128–137 (1990)Google Scholar
  7. 7.
    Fischer, F., Procaccia, A.D., Samorodnitsky, A.: On voting caterpillars:approximating maximum degree in a tournament by binary trees. In: COMSOC (2008)Google Scholar
  8. 8.
    Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41 (1973)Google Scholar
  9. 9.
    Hazon, N., Dunne, P.E., Kraus, S., Wooldridge, M.: How to rig elections and competitions. In: COMSOC (2008)Google Scholar
  10. 10.
    Lang, J., Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Winner determination in sequential majority voting. In: IJCAI (2007)Google Scholar
  11. 11.
    Russell, T.: A computational study of problems in sports. University of Waterloo PhD Disseration (2010)Google Scholar
  12. 12.
    Russell, T., Walsh, T.: Manipulating tournaments in cup and round robin competitions. In: Algorithmic Decision Theory (2009)Google Scholar
  13. 13.
    Satterthwaite, M.A.: Strategy-proofness and arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10 (1975)Google Scholar
  14. 14.
    Slater, P.: Inconsistencies in a schedule of paired comparisons. Biometrika 48(3/4), 303–312 (1961)CrossRefGoogle Scholar
  15. 15.
    Stanton, I., Vassilevska Williams, V.: Rigging tournament brackets for weaker players. In: IJCAI (2011)Google Scholar
  16. 16.
    Vassilevska Williams, V.: Fixing a tournament. In: AAAI, pp. 895–900 (2010)Google Scholar
  17. 17.
    Vu, T., Altman, A., Shoham, Y.: On the complexity of schedule control problems for knockout tournaments. In: AAMAS (2009)Google Scholar
  18. 18.
    Vu, T., Hazon, N., Altman, A., Kraus, S., Shoham, Y., Wooldridge, M.: On the complexity of schedule control problems for knock-out tournaments. In: JAIR (2010)Google Scholar
  19. 19.
    Young, H.P.: Condorcets theory of voting. The American Political Science Review 82(4), 1231–1244 (1988)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Isabelle Stanton
    • 1
  • Virginia Vassilevska Williams
    • 1
  1. 1.Computer Science DepartmentUC BerkeleyUSA

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