Cycles in team tennis and other paired-element contests

Shane Sanders, Justin Ehrlich, James Boudreau

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number27
JournalGames
Volume8
Issue number3
DOIs
StatePublished - Sep 2017

Keywords

  • Competitive balance
  • Ranking cycles
  • Social choice theory
  • Sports
  • Strategic voting

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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