Foundations of Spatial Preferences - NYU.pdf

Foundations of Spatial Preferences∗ Jon X Eguia† New York University April 1, 2009 Abstract I provide an axiomatic foundation for the assumption of specific utility func- tions in a multidimensional spatial model, endogenizing the spatial representa- tion of the set of alternatives. Given a set of objects with multiple attributes, I find simple necessary and sufficient conditions on preferences such that there exists a mapping of the set of objects into a Euclidean space where the utility function of the agent is linear city block, quadratic Euclidean, or more gener- ally, it is the δ power of one of Minkowski’s [25] metric functions. In a society with multiple agents, I characterize the set of preferences that are representable by weighted versions of a family of functions that are indexed by a parameter δ0, where δ ≥1 corresponds to the set of Minkowski’s functions. In light of the starkly different consequences between representability with δ ≤1 or with δ1,I propose a test to empirically estimate δ. JEL Classification: D81, D72. Keywords: Utility representation, spatial models, multidimensional pref- erences, spatial representation. ∗Macartan Humphreys provided crucial ideas for this paper, and I am accordingly grateful to him. I also thank Miguel Ángel Ballester, Salvador Barberà, Dimitri Landa, Jean-François Laslier, Michael Laver, Jordi Massó, Wolfgang Pesendorfer and participants at seminars at UC Berkeley, U. Malaga and Rutgers U. for their valuable comments and suggestions. I wrote a first draft while visiting the Dept. of Economics at U. Autònoma de Barcelona, where I enjoyed an ideal research environment.