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Banks winners in tournaments are difficult to recognize

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  • Gerhard J. Woeginger

Abstract

Given a tournament T, a Banks winner of T is the top vertex of any maximal (with respect to inclusion) transitive subtournament of T. In this technical note, we show that the problem of deciding whether some fixed vertex v is a Banks winner for T is NP-complete. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:20:y:2003:i:3:p:523-528
    DOI: 10.1007/s003550200197
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    Cited by:

    1. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    2. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Scott Moser & John W. Patty & Elizabeth Maggie Penn, 2009. "The Structure of Heresthetical Power," Journal of Theoretical Politics, , vol. 21(2), pages 139-159, April.
    4. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    5. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    6. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
    7. Brandt, Felix & Harrenstein, Paul & Seedig, Hans Georg, 2017. "Minimal extending sets in tournaments," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 55-63.
    8. Felix Brandt & Markus Brill & Paul Harrenstein, 2018. "Extending tournament solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 193-222, August.
    9. Fabrice Talla Nobibon & Laurens Cherchye & Yves Crama & Thomas Demuynck & Bram De Rock & Frits C. R. Spieksma, 2016. "Revealed Preference Tests of Collectively Rational Consumption Behavior: Formulations and Algorithms," Operations Research, INFORMS, vol. 64(6), pages 1197-1216, December.
    10. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    11. Felix Brandt & Florian Grundbacher, 2023. "The Banks Set and the Bipartisan Set May Be Disjoint," Papers 2308.01881, arXiv.org, revised Oct 2024.
    12. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    13. Yongjie Yang & Jiong Guo, 2017. "Possible winner problems on partial tournaments: a parameterized study," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 882-896, April.
    14. Scott Moser, 2015. "Majority rule and tournament solutions," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 6, pages 83-101, Edward Elgar Publishing.
    15. Felix Brandt & Markus Brill & Felix Fischer & Paul Harrenstein, 2014. "Minimal retentive sets in tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 551-574, March.
    16. Fujun Hou, 2024. "A new social welfare function with a number of desirable properties," Papers 2403.16373, arXiv.org.
    17. Hudry, Olivier, 2010. "On the complexity of Slater's problems," European Journal of Operational Research, Elsevier, vol. 203(1), pages 216-221, May.

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