Is Computational Complexity a Barrier to Manipulation?

TL;DR

This paper investigates whether computational complexity genuinely prevents manipulation in voting systems by examining empirical phase transitions, revealing that complexity may not be an effective barrier in practice.

Contribution

It introduces an empirical approach using phase transitions to assess the practical difficulty of manipulating voting rules, challenging the assumption that NP-hardness blocks manipulation.

Findings

Phase transition analysis reveals manipulation can be computationally easy in practice.

NP-hardness may not serve as an effective barrier to manipulation.

Insights extend to related problems like stable marriage and tournaments.

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, NP-hardness 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.