Obvious Manipulability of Voting Rules
This work addresses the problem of designing more practical voting rules for social choice theory by relaxing strategyproofness assumptions, though it is incremental as it builds on existing concepts.
The paper revisits voting rules by applying the weaker notion of not obvious manipulability, identifying classes of rules that satisfy it and showing that others like k-approval fail, with insights on conditions like large alternatives relative to voters leading to obvious manipulability.
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.