A reformulation of Chichilnisky's impossibility theorem (Q908825)

\textit{G. Chichilnisky}'s impossibility theorem [ibid. 3, No.4, 347-351 (1979; Zbl 0693.90008] states that there is no continuous social welfare function which is anonymous and respects unanimity. Given a topology on the space of preferences, continuity is taken relative to the product topology for profiles (n-tuples of preferences). However, anonymity itself provides the basis for a different approach to continuity. That is, if anonymity is really thought to be a desirable property of social choice, then one must accept an approach to continuity different from Chichilnisky's. However, as shown in this paper, Chichilnisky's impossibility still persits.