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Cycles in Team Tennis and Other Paired-Element Contests

Shane Sanders (), Justin Ehrlich () and James Boudreau ()
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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

Games, 2017, vol. 8, issue 3, 1-14

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.

Keywords: social choice theory; competitive balance; ranking cycles; strategic voting; sports (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2017
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