Obvious Manipulability of Voting Rules

TL;DR

This paper explores a weaker form of strategyproofness called not obvious manipulability in voting rules, identifying classes that satisfy it, and analyzing when rules are obviously manipulable, with algorithmic and experimental insights.

Contribution

It introduces and characterizes the concept of not obvious manipulability, expanding understanding beyond strategyproofness and providing algorithmic tools and experimental results.

Findings

Certain voting rules are not obviously manipulable.

Rules become obviously manipulable with many alternatives relative to voters.

Algorithmic methods for computing obvious manipulations are developed.

Abstract

The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by Troyan and Morrill (2020). We identify several classes of voting rules that satisfy this notion. We also show that several voting rules including k-approval fail to satisfy this property. We characterize conditions under which voting rules are obviously manipulable. One of our insights is that certain rules are obviously manipulable when the number of alternatives is relatively large compared to the number of voters. In contrast to the Gibbard-Satterthwaite theorem, many of the rules we examined are not obviously manipulable. This reflects the relatively easier satisfiability of the notion and the zero information assumption of not obvious manipulability, as opposed to the perfect information assumption of strategyproofness. We also present algorithmic results for computing obvious manipulations and report on experiments.