More on Decision Rules and Policy Outcomes

An attempt to rationalize policy outcomes in voting bodies has been made by Rae and Taylor (this Journal, 1 (1971), 71–90). In that work the assumption is made that all voters' preferences are representable by ‘city block' type utility functions. The principal result obtained in that case by the writers is that for an odd number of voters there is always a unique equilibrium point under simple majority rule, independent of the distribution of individual optimal points and independent of the dimension of the policy space. Unfortunately, the Rae and Taylor result is not correct. In particular their result holds for a one or two dimensional policy space but not in cases where the policy space has three or more dimensions. The proof given by Rae and Taylor is correct for n = 2 but is false for n ≥ 3.