Remember Me
Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:

OpenAIRE is about to release its new face with lots of new content and services.
During September, you may notice downtime in services, while some functionalities (e.g. user registration, login, validation, claiming) will be temporarily disabled.
We apologize for the inconvenience, please stay tuned!
For further information please contact helpdesk[at]openaire.eu

fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Brandt, Felix; Brill, Markus; Fischer, Felix; Harrenstein, Paul (2014)
Publisher: Springer
Languages: English
Types: Article
Tournament solutions, i.e., functions that associate with each complete and asymmetric relation on a set of alternatives a nonempty subset of the alternatives, play an important role in the mathematical social sciences at large. For any given tournament solution S, there is another tournament solution  which returns the union of all inclusion-minimal sets that satisfy S-retentiveness, a natural stability criterion with respect to S. Schwartz’s tournament equilibrium set (TEQ) is defined recursively as . In this article, we study under which circumstances a number of important and desirable properties are inherited from S to . We thus obtain a hierarchy of attractive and efficiently computable tournament solutions that “approximate” TEQ, which itself is computationally intractable. We further prove a weaker version of a recently disproved conjecture surrounding TEQ, which establishes —a refinement of the top cycle—as an interesting new tournament solution.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • F. Brandt and F. Fischer. Computing the minimal covering set. Mathematical Social Sciences, 56(2):254-268, 2008.
    • F. Brandt and P. Harrenstein. Characterization of dominance relations in finite coalitional games. Theory and Decision, 69(2):233-256, 2010.
    • F. Brandt and P. Harrenstein. Set-rationalizable choice and self-stability. Journal of Economic Theory, 146(4):1721-1731, 2011.
    • F. Brandt, F. Fischer, and P. Harrenstein. The computational complexity of choice sets. Mathematical Logic Quarterly, 55(4):444-459, 2009.
    • F. Brandt, F. Fischer, P. Harrenstein, and M. Mair. A computational analysis of the tournament equilibrium set. Social Choice and Welfare, 34(4):597-609, 2010.
    • F. Brandt, M. Chudnovsky, I. Kim, G. Liu, S. Norin, A. Scott, P. Seymour, and S. Thomasse´. A counterexample to a conjecture of Schwartz. Social Choice and Welfare, 2012. Forthcoming.
    • V. Conitzer. Computing Slater rankings using similarities among candidates. In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI), pages 613-619. AAAI Press, 2006.
    • J. Duggan and M. Le Breton. Dutta's minimal covering set and Shapley's saddles. Journal of Economic Theory, 70:257-265, 1996.
    • P. M. Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77:321-357, 1995.
    • P. E. Dunne. Computational properties of argumentation systems satisfying graphtheoretic constraints. Artificial Intelligence, 171(10-15):701-729, 2007.
    • B. Dutta. On the tournament equilibrium set. Social Choice and Welfare, 7(4):381- 383, 1990.
    • D. C. Fisher and J. Ryan. Tournament games and positive tournaments. Journal of Graph Theory, 19(2):217-236, 1995.
    • I. J. Good. A note on Condorcet sets. Public Choice, 10:97-101, 1971.
    • N. Houy. Still more on the tournament equilibrium set. Social Choice and Welfare, 32:93-99, 2009a.
    • N. Houy. A few new results on TEQ. Mimeo, 2009b.
    • G. La ond, J.-F. Laslier, and M. Le Breton. More on the tournament equilibrium set. Mathe´matiques et sciences humaines, 31(123):37-44, 1993a.
    • G. La ond, J.-F. Laslier, and M. Le Breton. The bipartisan set of a tournament game. Games and Economic Behavior, 5:182-201, 1993b.
    • G. La ond, J. Laine´, and J.-F. Laslier. Composition-consistent tournament solutions and social choice functions. Social Choice and Welfare, 13:75-93, 1996.
    • J.-F. Laslier. Tournament Solutions and Majority Voting. Springer-Verlag, 1997.
    • S. Moser. A note on contestation-based solution concepts. Mimeo, 2009.
    • H. Moulin. Choosing from a tournament. Social Choice and Welfare, 3:271-291, 1986.
    • T. Schwartz. Cyclic tournaments and cooperative majority voting: A solution. Social Choice and Welfare, 7:19-29, 1990.
    • G. J. Woeginger. Banks winners in tournaments are di cult to recognize. Social Choice and Welfare, 20:523-528, 2003.
  • No related research data.
  • No similar publications.

Share - Bookmark

Download from

Cite this article

Cookies make it easier for us to provide you with our services. With the usage of our services you permit us to use cookies.
More information Ok