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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. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    2. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    3. 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.
    4. 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.
    5. 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.
    6. Felix Brandt & Florian Grundbacher, 2023. "The Banks Set and the Bipartisan Set May Be Disjoint," Papers 2308.01881, arXiv.org, revised Oct 2024.
    7. 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.
    8. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
    9. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    10. 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.
    11. 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.
    12. 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.
    13. Brandt, Felix & Harrenstein, Paul & Seedig, Hans Georg, 2017. "Minimal extending sets in tournaments," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 55-63.
    14. 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.
    15. 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.
    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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