Foundations of spatial preferences

I provide an axiomatic foundation for the assumption of specific utility functions in a multidimensional spatial model, endogenizing the spatial representation 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 generally, it is the δ power of one of Minkowski (1886) metric functions. In a society with multiple agents I characterize the set of preferences that are representable by weighted linear city block utility functions, and I discuss how the result extends to other Minkowski utility functions.