Foundations of Spatial Preferences∗

I show that if an agent is risk neutral over a set of alternatives contained in a Euclidean space, then her utility function decreases linearly in the city block distance to her ideal point. Given a set of alternatives which is not contained in a Euclidean space, I find simple necessary and sufficient conditions on preferences such that, for any p ≥ 1, there exists a mapping of the set of alternatives into a Euclidean space where the utility of the agent is a decreasing function of the lp distance to her ideal point. City block and quadratic Euclidean utilities are the special cases p = 1 and p = 2. For these cases I extend the result to a society with multiple agents, finding additional conditions such that a common space exists in which the preferences of every agent are representable by city block utilities, or by quadratic Euclidean utilities. JEL Classification: D81, D72.