  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.
