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- W2410043267 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 $binom{n}{2}$ 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 (Altman and Kleinberg). 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." @default.
- W2410043267 created "2016-06-24" @default.
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- W2410043267 date "2016-05-31" @default.
- W2410043267 modified "2023-09-27" @default.
- W2410043267 title "Condorcet-Consistent and Approximately Strategyproof Tournament Rules" @default.
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