TY - GEN

T1 - Condorcet-consistent and approximately strategyproof tournament rules

AU - Schneider, Jon

AU - Schvartzman, Ariel

AU - Matthew Weinberg, S.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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.

AB - 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.

KW - Condorcet-consistent

KW - Non-manipulability

KW - Strategyproofness

KW - Tournament design

UR - http://www.scopus.com/inward/record.url?scp=85038572834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038572834&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ITCS.2017.35

DO - 10.4230/LIPIcs.ITCS.2017.35

M3 - Conference contribution

AN - SCOPUS:85038572834

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 8th Innovations in Theoretical Computer Science Conference, ITCS 2017

A2 - Papadimitriou, Christos H.

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 8th Innovations in Theoretical Computer Science Conference, ITCS 2017

Y2 - 9 January 2017 through 11 January 2017

ER -