A characterization of the uniform rule with several commodities and agents

We consider a problem of allocating infinitely divisible commodities among a group of agents. More specifically, there are several commodities to be allocated and agents have continuous, strictly convex, and separable preferences. We establish that a rule satisfies strategy-proofness, unanimity, weak symmetry, and nonbossiness if and only if it is the uniform rule. This result extends to the class of continuous, strictly convex, and multidimensional single-peaked preferences. Copyright Springer-Verlag 2013