Is computational complexity a barrier to manipulation?

Abstract

Abstract. 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 misreporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NPhardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational "phase transitions". Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems.

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

“…Our findings with the greedy heuristic suggest that there is reason to believe that Lobbying is computationally not so hard as worst-case analysis suggests. The situation is similar in the recent studies concerning the seemingly "pathological" NP-hardness of manipulation and its very good solvability in experimental results (Betzler, Niedermeier, & Woeginger, 2011;Davies, Katsirelos, Narodytska, & Walsh, 2011;Davies, Narodytska, & Walsh, 2012;Walsh, 2011). A more thorough investigation in this direction concerning Lobbying seems promising.…”

Solving hard control problems in voting systems via integer programming

“…On the other hand, if it is easy to manipulate the election structure to get one's favorite candidate to win, then this is regarded as negative in view of susceptibility to illegal influence. [Walsh, 2011] discusses the types of illegal influence. So, voting rules not only should be efficient, they also should be hard (ideally even impossible) to influence in an illegal way.…”

“…In the context of computational social choice, [Walsh, 2011] clearly demonstrates that NP-hardness is not a barrier to manipulations and illegal influences. [Conitzer and Sandholm, 2006] present a simple influence algorithm for elections that works fast and yields for most inputs (according to a suitably chosen probability distribution) the desired result.…”

Election Attacks with Few Candidates

“…Recently, this purely worst-case analysis, which ignores realworld settings, was criticized by researchers. See [4,12,20,26,28] for detailed discussions. For their purpose, they proposed diverse measurements to evaluate the feasibility of strategic behaviors in practical elections.…”