Social Choice and Welfare

, Volume 34, Issue 4, pp 597–609 | Cite as

A computational analysis of the tournament equilibrium set

  • Felix Brandt
  • Felix Fischer
  • Paul Harrenstein
  • Maximilian Mair
original paper

Abstract

A recurring theme in the mathematical social sciences is how to select the “most desirable” elements given a binary dominance relation on a set of alternatives. Schwartz’s tournament equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions proposed so far. Due to its unwieldy recursive definition, little is known about TEQ. In particular, its monotonicity remains an open problem to date. Yet, if TEQ were to satisfy monotonicity, it would be a very attractive solution concept refining both the Banks set and Dutta’s minimal covering set. We show that the problem of deciding whether a given alternative is contained in TEQ is NP-hard, and thus does not admit a polynomial-time algorithm unless P equals NP. Furthermore, we propose a heuristic that significantly outperforms the naive algorithm for computing TEQ.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Felix Brandt
    • 1
  • Felix Fischer
    • 1
  • Paul Harrenstein
    • 1
  • Maximilian Mair
    • 2
  1. 1.Institut für InformatikLudwig-Maximilians-Universität MünchenMunichGermany
  2. 2.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMunichGermany

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