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The Banks Set and the Bipartisan Set May Be Disjoint

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  • Felix Brandt
  • Florian Grundbacher

Abstract

Tournament solutions play an important role within social choice theory and the mathematical social sciences at large. We construct a tournament of order 36 for which the Banks set and the bipartisan set are disjoint. This implies that refinements of the Banks set, such as the minimal extending set and the tournament equilibrium set, can also be disjoint from the bipartisan set.

Suggested Citation

  • Felix Brandt & Florian Grundbacher, 2023. "The Banks Set and the Bipartisan Set May Be Disjoint," Papers 2308.01881, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2308.01881
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    1. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    2. Laffond G. & Laslier, J. F. & Le Breton, M., 1996. "Condorcet choice correspondences: A set-theoretical comparison," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 59-59, February.
    3. Gerhard J. Woeginger, 2003. "Banks winners in tournaments are difficult to recognize," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 523-528, June.
    4. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
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