Nonmanipulable Selections from a Tournament

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 the problem of the manipulation of choice rules by considering two types of manipulation. We say that a choice rule is monotonic if an alternative cannot get itself selected by losing on purpose, and 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.

[1]  Nicolas de Condorcet.  Essai Sur L'Application de L'Analyse a la Probabilite Des Decisions Rendues a la Pluralite Des Voix , 2009 .

[2]  V. S. Costa,et al.  Theory and Practice of Logic Programming , 2010 .

[3]  Yan Zhang,et al.  On the Semantics of Knowledge Update , 2001, IJCAI.

[4]  Chiaki Sakama,et al.  Updating Extended Logic Programs through Abduction , 1999, LPNMR.

[5]  Matthew O. Jackson,et al.  Voting by Successive Elimination and Strategic Candidacy , 2002, J. Econ. Theory.

[6]  Moshe Tennenholtz,et al.  Strategyproof deterministic lotteries under broadcast communication , 2008, AAMAS.

[7]  Jorge Lobo,et al.  Knowledge and the Action Description Language A , 2001, Theory Pract. Log. Program..

[8]  Hans Tompits,et al.  A Framework for Declarative Update Specifications in Logic Programs , 2001, IJCAI.

[9]  Iyad Rahwan,et al.  Mechanism design for abstract argumentation , 2008, AAMAS.

[10]  Richard Watson.  A Splitting Set Theorem for Epistemic Specifications , 2000, ArXiv.

[11]  Hirofumi Katsuno,et al.  On the Difference between Updating a Knowledge Base and Revising It , 1991, KR.

[12]  Jean-François Laslier,et al.  Tournament Solutions And Majority Voting , 1997 .

[13]  Yan Zhang.  Minimal Change and Maximal Coherence for Epistemic Logic Program Updates , 2003, IJCAI.

[14]  Marianne Winslett,et al.  Reasoning about Action Using a Possible Models Approach , 1988, AAAI.

[15]  Jörg Rothe,et al.  Anyone but him: The complexity of precluding an alternative , 2005, Artif. Intell..

[16]  Paul E. Dunne,et al.  Computational properties of argument systems satisfying graph-theoretic constraints , 2007, Artif. Intell..

[17]  Vladimir Lifschitz,et al.  Splitting a Logic Program , 1994, ICLP.

[18]  Michael Gelfond,et al.  Logic programming and reasoning with incomplete information , 1994, Annals of Mathematics and Artificial Intelligence.

[19]  Vincent Conitzer,et al.  When are elections with few candidates hard to manipulate? , 2007, J. ACM.

[20]  José Júlio Alferes,et al.  Dynamic updates of non-monotonic knowledge bases , 2000, J. Log. Program..

[21]  Norman Y. Foo,et al.  Updating Logic Programs , 1998, ECAI.

[22]  Ariel D. Procaccia,et al.  Junta Distributions and the Average-Case Complexity of Manipulating Elections , 2007, J. Artif. Intell. Res..

[23]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[24]  Phan Minh Dung,et al.  On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games , 1995, Artif. Intell..

[25]  Ariel D. Procaccia,et al.  Extensive-Form Argumentation Games , 2005, EUMAS.

[26]  Thierry Marchant,et al.  Evaluation and Decision Models with Multiple Criteria: Stepping Stones for the Analyst , 2006 .

[27]  Felix A. Fischer,et al.  A computational analysis of the tournament equilibrium set , 2008, Soc. Choice Welf..

[28]  Hans Tompits,et al.  On properties of update sequences based on causal rejection , 2001, Theory and Practice of Logic Programming.

[29]  David C. Mcgarvey.  A THEOREMI ON THE CONSTRUCTION OF VOTING PARADOXES , 1953 .