Arrow’s impossibility theorem considers elections involving at least three candidates. Each voter ranks all candidates, and the votes are aggregated on a (candidate-)pairwise basis. Arrow showed that under the mild condition of unanimity, the only valid aggregation rules are dictatorships. Kalai showed that even if validity only holds with probability close to 1, the aggregation rule has to be close to a dictatorship.

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We describe a novel framework for proving such results, and use it to prove two results on classification aggregation. No knowledge of social choice theory or judgment aggregation will be required to follow the talk.

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Partially based on joint work with Yaroslav Alekseev.