Nonmanipulable Selections from a Tournament

Alon Altman, Ariel D. Procaccia, Moshe Tennenholtz, Felix Brandt, Vincent Conitzer, Lane A. Hemaspaandra, Jean-Francois Laslier, William S. Zwicker
A tournament is a binary dominance relation on a set of alternatives. Tournaments arise in many contexts that are relevant to AI, most notably in voting (as a method to aggregate the preferences of agents). There are many works that deal with choice rules that select a desirable alternative from a tournament, but very few of them deal directly with incentive issues, despite the fact that game-theoretic considerations are crucial with respect to systems populated by selfish agents. We deal with
more » ... he problem of the manipulation of choice rules by considering two types of manipulation. We say that a choice rule is emph{monotonic} if an alternative cannot get itself selected by losing on purpose, and emph{pairwise nonmanipulable} if a pair of alternatives cannot make one of them the winner by reversing the outcome of the match between them. Our main result is a combinatorial construction of a choice rule that is monotonic, pairwise nonmanipulable, and onto the set of alternatives, for any number of alternatives besides three.
doi:10.4230/dagsemproc.10101.5 fatcat:6xnlztcsgvckjfvrtr6wbas2se