Dictatorship on top-circular domains

We consider domains with a natural property called top-circularity. We show that if such a domain satisfies either the maximal conflict property or the weak conflict property, then it is dictatorial. We obtain the result in Sato (Rev Econ Des 14(3):331–342, 2010) as a corollary. Furthermore, it follows from our results that the union of a single-peaked domain and a single-dipped domain (with respect to a given ordering over the alternatives) is dictatorial.

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