Dictatorship on Top-circular Domains

Abstract

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 (2010) as a corollary. Further, it follows from our results that the union of a top-connected single-peaked domain and a top-connected single-dipped domain is dictatorial