Abstract. We introduce the notion of obvious manipulation by groups,
extending obvious manipulability from individual to coalitional
deviations. While existing work focuses on individual incentives,
coordinated deviations are often natural, calling for a notion of
obviousness at the group level.
We propose a definition based on
simple best- and worst-case reasoning and study its implications for
voting rules. In tops-only domains, ruling out obvious group
manipulations imposes strong restrictions: it implies efficiency,
monotonicity, and an almost-unanimity property.
Our main result
shows that any tops-only, monotonic voting rule that is not obviously
manipulable by groups must be dictatorial. This is somewhat surprising
in light of the positive results for individual non-obvious
manipulability, where rich classes of rules can be sustained. By
contrast, robustness to obvious group deviations sharply limits the
design of voting rules.
We also show that many standard rules
satisfying the majority criterion are vulnerable to obvious group
manipulations. Overall, our results provide a first step toward a theory
of group obviousness and uncover new tensions between collective
incentives and classical voting principles.
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