We investigate a social choice function that satisfies anonymity, spatial neutrality, and Maskin monotonicity in a multidimensional spatial model where each agent has an ideal point and prefers a point with a shorter rectilinear distance ( \(L_1\) -distance) from it. In this model, the \(L_1\) -median of agents’ ideal points coincides with the coordinate-wise median of these points with respect to the standard orthogonal coordinate system when there are an odd number of agents. Based on this fact, we show that the \(L_1\) -median function is the only social choice function that satisfies anonymity, spatial neutrality, and Maskin monotonicity when there are an odd number of agents. Furthermore, we show that there exists no social choice function that satisfies these three conditions when there are an even number of agents.
