Algorithms for the coalitional manipulation problem

We investigate the problem of coalitional manipulation in elections, which is known to be hard in a variety of voting rules. We put forward efficient algorithms for the problem in Scoring rules, Maximum and Plurality with runoff, and analyze their windows of error. Specifically, given an instance on which an algorithm fails, we bound the additional power the manipulators need in order to succeed. We finally discuss the implications of our results with respect to the popular approach of employing computational hardness to preclude manipulation.

[1]  Vincent Conitzer,et al.  Nonexistence of Voting Rules That Are Usually Hard to Manipulate , 2006, AAAI.

[2]  H. Moulin.  On strategy-proofness and single peakedness , 1980 .

[3]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[4]  Noam Nisan,et al.  Elections Can be Manipulated Often , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[5]  W. K. Vickery,et al.  Counter-Speculation Auctions and Competitive Sealed Tenders , 1961 .

[6]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

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

[8]  John J. Bartholdi,et al.  Single transferable vote resists strategic voting , 2015 .

[9]  Arkadii M. Slinko,et al.  How large should a coalition be to manipulate an election? , 2004, Math. Soc. Sci..

[10]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[11]  Z. Neeman,et al.  The asymptotic strategyproofness of scoring and Condorcet consistent rules , 2002 .

[12]  Martin Grohe.  The complexity of homomorphism and constraint satisfaction problems seen from the other side , 2007, JACM.

[13]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[14]  Sandip Sen,et al.  Voting for movies: the anatomy of a recommender system , 1999, AGENTS '99.

[15]  Edith Elkind,et al.  Small Coalitions Cannot Manipulate Voting , 2005, Financial Cryptography.

[16]  Piotr Faliszewski,et al.  The Complexity of Bribery in Elections , 2006, AAAI.

[17]  Edith Elkind,et al.  Hybrid Voting Protocols and Hardness of Manipulation , 2005, ISAAC.

[18]  Sandip Sen,et al.  An automated meeting scheduling system that utilizes user preferences , 1997, AGENTS '97.

[19]  Inon Zuckerman,et al.  Universal Voting Protocol Tweaks to Make Manipulation Hard , 2003, IJCAI.

[20]  Georgios Paliouras,et al.  Combining Information Extraction Systems Using Voting and Stacked Generalization , 2005, J. Mach. Learn. Res..

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

[22]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[23]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[24]  Eithan Ephrati,et al.  A heuristic technique for multi‐agent planning , 1997, Annals of Mathematics and Artificial Intelligence.

[25]  Jörg Rothe,et al.  On Approximating Optimal Weighted Lobbying, and Frequency of Correctness Versus Average-Case Polynomial Time , 2007, FCT.

[26]  Ariel D. Procaccia,et al.  Average-case tractability of manipulation in voting via the fraction of manipulators , 2007, AAMAS '07.

[27]  Ariel D. Procaccia,et al.  Junta distributions and the average-case complexity of manipulating elections , 2006, AAMAS '06.

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

[29]  M. Trick,et al.  Voting schemes for which it can be difficult to tell who won the election , 1989 .

[30]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[31]  Eric Horvitz,et al.  Social Choice Theory and Recommender Systems: Analysis of the Axiomatic Foundations of Collaborative Filtering , 2000, AAAI/IAAI.

[32]  Gökhan Tür,et al.  Morphological Disambiguation by Voting Constraints , 1997, ACL.

[33]  Ariel D. Procaccia,et al.  Multi-Winner Elections: Complexity of Manipulation, Control and Winner-Determination , 2007, IJCAI.

[34]  E. Ephrati.  A Heuristic Technique for Multiagent PlanningEithan , 1997 .