Annals of Mathematics and Artificial Intelligence

, Volume 62, Issue 1, pp 7–26

Is computational complexity a barrier to manipulation?


DOI: 10.1007/s10472-011-9255-9

Cite this article as:
Walsh, T. Ann Math Artif Intell (2011) 62: 7. doi:10.1007/s10472-011-9255-9


When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by mis-reporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. In this survey article, we summarize the evidence for and against computational complexity being a barrier to manipulation. We look both at techniques identified to increase complexity (for example, hybridizing together two or more voting rules), as well as other features that may change the computational complexity of computing a manipulation (for example, if votes are restricted to be single peaked then some of the complexity barriers fall away). We discuss recent theoretical results that consider the average case, as well as simple greedy and approximate methods. We also describe how computational “phase transitions”, which have been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems, have provided insight into the hardness of manipulating voting rules in practice. Finally, we consider manipulation of other related problems like stable marriage and tournament problems.


Social choiceManipulationComputational complexityStable marriage

Mathematics Subject Classifications (2010)


Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.NICTA and University of NSWSydneyAustralia