More on the preservation of preference proximity and anonymous social choice

Using a finite social choice framework, Baigent [1987], following Chichilnisky's [1982] topological approach, has considered a proximity preservation property for social welfare functions and social choice functions. This property requires that the" smaller the change" in individual preferences, the" smaller the change" in social preference or in the social choice. It has been shown that if a social welfare function or a social choice function has such a proximity preservation property, then it cannot both respect unanimity and be anonymous.