Abstract
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.
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References
Bartholdi, J., Tovey, C., Trick, M.: The computational difficulty of manipulating an election. Social Choice Welfare 6(3), 227–241 (1989)
Bartholdi, J., Tovey, C., Trick, M.: How hard is it to control an election. Mathematical and Computer Modeling, 27–40 (1992)
Braverman, M., Mossel, E.: Noisy sorting without resampling. In: SODA, pp. 268–276 (2008)
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)
Erdős, P., Rényi, A.: On random matrices. Publications of the Mathematical Institute Hungarian Academy of Science 8, 455–561 (1964)
Feige, U., Peleg, D., Laghavan, P., Upfal, E.: Computing with unreliable information. In: STOC, pp. 128–137 (1990)
Fischer, F., Procaccia, A.D., Samorodnitsky, A.: On voting caterpillars:approximating maximum degree in a tournament by binary trees. In: COMSOC (2008)
Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41 (1973)
Hazon, N., Dunne, P.E., Kraus, S., Wooldridge, M.: How to rig elections and competitions. In: COMSOC (2008)
Lang, J., Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Winner determination in sequential majority voting. In: IJCAI (2007)
Russell, T.: A computational study of problems in sports. University of Waterloo PhD Disseration (2010)
Russell, T., Walsh, T.: Manipulating tournaments in cup and round robin competitions. In: Algorithmic Decision Theory (2009)
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)
Slater, P.: Inconsistencies in a schedule of paired comparisons. Biometrika 48(3/4), 303–312 (1961)
Stanton, I., Vassilevska Williams, V.: Rigging tournament brackets for weaker players. In: IJCAI (2011)
Vassilevska Williams, V.: Fixing a tournament. In: AAAI, pp. 895–900 (2010)
Vu, T., Altman, A., Shoham, Y.: On the complexity of schedule control problems for knockout tournaments. In: AAMAS (2009)
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)
Young, H.P.: Condorcets theory of voting. The American Political Science Review 82(4), 1231–1244 (1988)
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Stanton, I., Vassilevska Williams, V. (2011). Manipulating Stochastically Generated Single-Elimination Tournaments for Nearly All Players. In: Chen, N., Elkind, E., Koutsoupias, E. (eds) Internet and Network Economics. WINE 2011. Lecture Notes in Computer Science, vol 7090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25510-6_28
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DOI: https://doi.org/10.1007/978-3-642-25510-6_28
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