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Condorcet-Consistent and Approximately Strategyproof Tournament Rules

Author(s): Schneider, Jon; Schvartzman, Ariel; Weinberg, S Matthew

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Abstract: 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 n(n-1)/2 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 Condorcet-consistent rule is manipulable. 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 alpha-manipulable for any alpha > 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.
Publication Date: 2017
Citation: Schneider, Jon, Ariel Schvartzman, and S. Matthew Weinberg. "Condorcet-Consistent and Approximately Strategyproof Tournament Rules." In 8th Innovations in Theoretical Computer Science Conference (ITCS) (2017): 35:1-35:20. doi:10.4230/LIPIcs.ITCS.2017.35
DOI: 10.4230/LIPIcs.ITCS.2017.35
ISSN: 1868-8969
Pages: 35:1 - 35:20
Type of Material: Conference Article
Journal/Proceeding Title: 8th Innovations in Theoretical Computer Science Conference (ITCS)
Version: Final published version. This is an open access article.

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