On Strategic Control

The purpose of this note is to clarify and complement several comments on my work [Chichilnisky, 1980, 1982a], which appeared in this Journal: Baigent [1987], Nitzan [1989], and Baigent [1989]. I shall offer two new results. The first result constructs a continuous, anonymous social selection rule that respects unanimity and the proximity of preferences, for a large family of preferences (Theorem 1). This complements the result of Nitzan [1989] and Baigent's [1989] extension of it and is achieved by accepting, as they do, that social outcomes be optimal choices, rather than rankings of all possible choices or social preferences This result is of interest because it appears to contradict the original impossibility theorem of Chichilnisky, which establishes that, for the same family of preferences, social aggregation rules with these properties do not exist (Theorem 2)