We consider the problems where individuals classify objects into categories, and an aggregation function associates a social classification with any profile of individual classifications. Maniquet and Mongin (2016) delivered an Arrow-like impossibility theorem: If a classification aggregation function satisfies independence and unanimity, then it is dictatorial. In this paper, we first complete this Arrovian picture by providing proofs that cover the left out cases. This is achieved via a Wilson-type theorem, which shows the importance of unanimity by replacing it with citizen sovereignty (Wilson, 1972). We then move on to the problem of anonymous and neutral aggregation, and deliver a Moulin-type result (Moulin, 1983) that establishes the difficulty of reconciling these two conditions. We argue that insights from social choice theory can improve our understanding of classification aggregation problems.

Co-authored with Olivier Cailloux, Matthieu Hervouin, and Remzi Sanver 

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