Skip to main content
SpringerLink
Log in

A note on contestation-based tournament solutions

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

In tournaments, one alternative contests another if is a “winner” among only alternatives that beat it. This paper examines the consequences and limitations of the contestation relation by considering a procedure in which alternatives that are contested are iteratively eliminated from consideration. In doing so, a new family of tournament solutions are introduced and related to existing refinements of the Banks set. Findings show that iterated removal of contested alternatives a limited device for choosing from tournaments. These results contrast with results regarding the top-set of the contestation relation. Results highlight the role of the top-set operator for choice from tournaments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Banks JS (1985) Sophisticated voting outcomes and agenda control. Soc Choice Welf 1(4): 295–306

    Article  Google Scholar 

  • Brandt F, Brill M, Fischer F, Harrenstein P (2010a) Minimal retentive sets in tournaments. In: van der Hoek K, Luck S, (eds) Proceedings of 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), Toronto

  • Brandt F, Chudnovsky M, Kim I, Norin S, Scott A, Seymour P, Thomassé S, Montpelier F (2011) A counterexample to a conjecture of Schwartz. Soc Choice Welf (forthcoming)

  • Brandt F, Fischer F, Harrenstein P (2009) The computational complexity of choice sets. Math Log Quart 55(4): 444–459

    Article  Google Scholar 

  • Brandt F, Fischer F, Harrenstein P, Mair M (2010) A computational analysis of the tournament equilibrium set. Soc Choice Welf 34(4): 597–609

    Article  Google Scholar 

  • Dutta B (1990) On the tournament equilibrium set. Soc Choice Welf 7(4): 381–383

    Article  Google Scholar 

  • Houy N (2009) Still more on the tournament equilibrium set. Soc Choice Welf 32(1): 93–99

    Article  Google Scholar 

  • Laffond G, Laslier J, Le Breton M (1993) More on the tournament equilibrium set. Mathematiques et Sci Humaines 31(123): 37–44

    Google Scholar 

  • Laslier J-F (1997) Solutions and majority voting. Springer, Berlin

    Book  Google Scholar 

  • Moser S, Patty JW, Penn EM (2009) The structure of heresthetical power. J Theor Polit 21(2): 139–159

    Article  Google Scholar 

  • Schwartz T (1990) Cyclic tournaments and cooperative majority voting: a solution. Soc Choice Welf 7(1): 19–29

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Government, University of Texas at Austin, Austin, USA

    Scott Moser

Authors
  1. Scott Moser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Scott Moser.

Additional information

This work benefited greatly from the comments of two anonymous reviewers as well as associate editor Prof. Laslier. Any remaining errors are, of course, mine alone. A significant portion of this work was conducted while I was a Post-doctoral Research Fellow at Nuffield College, University of Oxford, to which I am most grateful.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moser, S. A note on contestation-based tournament solutions. Soc Choice Welf 41, 133–143 (2013). https://doi.org/10.1007/s00355-012-0672-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-012-0672-4

Keywords

Search

Navigation