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Cycles in Team Tennis and Other Paired-Element Contests

Author

Listed:
  • Shane Sanders

    () (Department of Sport Management, Falk College of Sport and Human Dynamics, Syracuse University, 301 MacNaughton Hall Syracuse, Syracuse, NY 13244, USA)

  • Justin Ehrlich

    () (Department of Computer Science, Western Illinois University, 447P Stipes Hall, Macomb, IL 61455, USA)

  • James Boudreau

    () (Department of Economics and Finance, Robert C. Vackar College of Business & Entrepreneurship, University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA)

Abstract

Team Tennis competitions produce aggregate scores for teams, and thus team rankings, based on head-to-head matchups of individual team members. Similar scoring rules can be used to rank any two groups that must be compared on the basis of paired elements. We explore such rules in terms of their strategic and social choice characteristics, with particular emphasis on the role of cycles. We first show that cycles play an important role in promoting competitive balance, and show that cycles allow for a maximum range of competitive balance within a league of competing teams. We also illustrate the impact that strategic behavior can have on the unpredictability of competition outcomes, and show for a general class of team tennis scoring rules that a rule is strategy-proof if and only if it is acyclic (dictatorial) and manipulable otherwise. Given the benefits of cycles and their relationship with manipulability, a league valuing competitive balance may invite such social choice violations when choosing a scoring rule.

Suggested Citation

  • Shane Sanders & Justin Ehrlich & James Boudreau, 2017. "Cycles in Team Tennis and Other Paired-Element Contests," Games, MDPI, Open Access Journal, vol. 8(3), pages 1-14, June.
  • Handle: RePEc:gam:jgames:v:8:y:2017:i:3:p:27-:d:103200
    as

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    References listed on IDEAS

    as
    1. Boudreau, James W. & Sanders, Shane, 2015. "Choosing “Flawed” aggregation rules: The benefit of social choice violations in a league that values competitive balance," Economics Letters, Elsevier, vol. 137(C), pages 106-108.
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    8. Boudreau, James & Ehrlich, Justin & Sanders, Shane & Winn, Adam, 2014. "Social choice violations in rank sum scoring: A formalization of conditions and corrective probability computations," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 20-29.
    9. Glenn Knowles & Keith Sherony & Mike Haupert, 1992. "The Demand for Major League Baseball: A Test of the Uncertainty of Outcome Hypothesis," The American Economist, Sage Publications, vol. 36(2), pages 72-80, October.
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    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    social choice theory; competitive balance; ranking cycles; strategic voting; sports;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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