1 research outputs found
Condorcet-Consistent and Approximately Strategyproof Tournament Rules
We consider the manipulability of tournament rules for round-robin
tournaments of competitors. Specifically, competitors are competing for
a prize, and a tournament rule maps the result of all
pairwise matches (called a tournament, ) to a distribution over winners.
Rule is Condorcet-consistent if whenever wins all of her matches,
selects with probability .
We consider strategic manipulation of tournaments where player might
throw their match to player in order to increase the likelihood that one of
them wins the tournament. Regardless of the reason why chooses to do this,
the potential for manipulation exists as long as increases by
more than 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
and decrease in for any potential manipulating
pair.
We show that every Condorcet-consistent rule is in fact -manipulable,
and that selecting a winner according to a random single elimination bracket is
not -manipulable for any . We also show that many
previously studied tournament formats are all -manipulable, and the
popular class of Copeland rules (any rule that selects a player with the most
wins) are all in fact -manipulable, the worst possible. Finally, we consider
extensions to match-fixing among sets of more than two players.Comment: 20 page