On the spatial representation of preference profiles

Given a set of alternatives with multiple attributes, I characterize the set of preference profiles that are representable by weighted versions of a class of utility functions indexed by a parameter delta > 0, where delta a parts per thousand yen 1 corresponds to the set of Minkowski's (1886) metric functions. In light of the starkly different consequences between representability with delta a parts per thousand currency sign 1 or with delta > 1, I propose a test to empirically estimate delta and I discuss the theoretical and empirical implications for spatial models of political competition.