 Theorem (Dietrich and List 2007b; Dokow and Holzman 2010a; building on Nehring and Puppe 2002, Other Internet Resources): If \(X\) is non-simple, pair-negatable, and path-connected, there exists no judgment aggregation rule satisfying universal domain, collective rationality, independence, unanimity preservation (requiring that, for any unanimous profile \(\langle J, J, \ldots ,J\rangle,\) \(F(J, J, \ldots ,J) = J)\), and  non-dictatorship.[13]