Condorcet-consistent and approximately strategyproof tournament rules

Jon Schneider, Ariel Schvartzman, S. Matthew Weinberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


We consider the manipulability of tournament rules for round-robin tournaments of n competitors. Specifically, n competitors are competing for a prize, and a tournament rule r maps the result of all (n2) pairwise matches (called a tournament, T) to a distribution over winners. Rule r is Condorcet-consistent if whenever i wins all n - 1 of her matches, r selects i with probability 1. We consider strategic manipulation of tournaments where player j might throw their match to player i in order to increase the likelihood that one of them wins the tournament. Regardless of the reason why j chooses to do this, the potential for manipulation exists as long as Pr[r(T) = i] increases by more than Pr[r(T) = j] decreases. Unfortunately, it is known that every Condorcetconsistent rule is manipulable [1]. In this work, we address the question of how manipulable Condorcet-consistent rules must necessarily be-by trying to minimize the difference between the increase in Pr[r(T) = i] and decrease in Pr[r(T) = j] for any potential manipulating pair. We show that every Condorcet-consistent rule is in fact 1/3-manipulable, and that selecting a winner according to a random single elimination bracket is not α-manipulable for any α > 1/3. We also show that many previously studied tournament formats are all 1/2-manipulable, and the popular class of Copeland rules (any rule that selects a player with the most wins) are all in fact 1-manipulable, the worst possible. Finally, we consider extensions to match-fixing among sets of more than two players.

Original languageEnglish (US)
Title of host publication8th Innovations in Theoretical Computer Science Conference, ITCS 2017
EditorsChristos H. Papadimitriou
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770293
StatePublished - Nov 1 2017
Event8th Innovations in Theoretical Computer Science Conference, ITCS 2017 - Berkeley, United States
Duration: Jan 9 2017Jan 11 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Other8th Innovations in Theoretical Computer Science Conference, ITCS 2017
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Software


  • Condorcet-consistent
  • Non-manipulability
  • Strategyproofness
  • Tournament design

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