Complexity of Strategic Behavior in Multi-Winner Elections

Although recent years have seen a surge of interest in the computational aspects of social choice, no specific attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we characterize the worst-case complexity of manipulation and control in the context of four prominent multiwinner voting systems, under different formulations of the strategic agent's goal.

[1]  Jérôme Lang,et al.  Vote and Aggregation in Combinatorial Domains with Structured Preferences , 2007, IJCAI.

[2]  Ulrich Endriss.  Vote manipulation in the presence of multiple sincere ballots , 2007, TARK '07.

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

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

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

[6]  John Duggan,et al.  Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized , 2000, Soc. Choice Welf..

[7]  Edith Hemaspaandra,et al.  Dichotomy for voting systems , 2005, J. Comput. Syst. Sci..

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

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

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

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

[12]  Vincent Conitzer,et al.  How many candidates are needed to make elections hard to manipulate? , 2003, TARK '03.

[13]  Ariel D. Procaccia,et al.  A broader picture of the complexity of strategic behavior in multi-winner elections , 2008, AAMAS.

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

[15]  Piotr Faliszewski,et al.  Llull and Copeland Voting Broadly Resist Bribery and Control , 2007, AAAI.

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

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

[18]  P. Fishburn,et al.  Voting Procedures , 2022 .

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

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

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

[22]  Ariel D. Procaccia,et al.  Algorithms for the coalitional manipulation problem , 2008, SODA '08.

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

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

[25]  Vincent Conitzer,et al.  Complexity of manipulating elections with few candidates , 2002, AAAI/IAAI.

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

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

[28]  Michael A. Trick,et al.  How hard is it to control an election? Math , 1992 .

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

[30]  Jörg Rothe,et al.  Hybrid Elections Broaden Complexity‐Theoretic Resistance to Control , 2006, IJCAI.

[31]  Deeparnab Chakrabarty,et al.  Knapsack Problems , 2008 .