On the Robustness of the Impossibility Result in the Topological Approach to Social Choice

In the first part we make an assessment of the impossibility result, due to Chichilnisky, in the topological approach to social choice theory. We observe that this result depends essentially on the choice of the topology for the set of preferences. In the second part, we present two positive results, obtained using the global approach. The first one deals with the space of continuous and strictly convex preferences, a space which, in the local approach, would produce an impossibility result. The second result deals with a class of preferences which is dense in the space of all continuous preferences. Thus, an approximate solution of the Chichilnisky problem has been obtained on this space.