Generalized location problems with n agents are considered, who each report a point in m-dimensional Euclidean space. A solution assigns a compromise point to these n points, and the individual utilities for this compromise point are equal to the negatives of the distances to the individual positions. These distances are measured by a given strictly convex norm, common to all agents. For m=2, it is shown that if a Pareto optimal, strategy-proof and anonymous solution exists, then n must be odd, and the solution is obtained by taking the median coordinatewise, where the coordinates refer to a basis that is orthogonal with respect to the given norm. Furthermore, in that case (m=2) such a solution always exists. For m>2, existence of a solution depends on the norm.
