An impossibility theorem for spatial models

This paper examines the implications for social welfare functions of restricting the domain of individual preferences to type-one preferences. Type-one preferences assume that each person has a most preferred alternative in a euclidean space and that alternatives are ranked according to their euclidean distance from this point. The result is that if we impose Arrow's conditions of collective rationality, IIA, and the Pareto principle on the social welfare function, then it must be dictatorial. This result may not seem surprising, but it stands in marked contrast to the problem considered by Gibbard and Satterthwaite of finding a social-choice function. With unrestricted domain, under the Gibbard-Satterthwaite hypotheses, choices must be dictatorial. With type-one preferences this result has been previously shown not to be true. This finding identifies a significant difference between the Arrow and Gibbard-Satterthwaite problems.