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 δ > 0, where δ ≥ 1 corresponds to the set of Minkowski’s (<CitationRef CitationID="CR34">1886</CitationRef>) metric functions. In light of the starkly different consequences between representability with δ ≤ 1 or with δ > 1, I propose a test to empirically estimate δ and I discuss the theoretical and empirical implications for spatial models of political competition. Copyright Springer-Verlag 2013