A characterization of the uniform rule based on new robustness properties

We study the problem of allocating a divisible good among a group of people. Each person’s preferences are single-peaked. We consider situations in which there might be more of the resource to be assigned than was planned, or there might be less of the resource. Two robustness properties are formulated, which we call one-sided composition up and one-sided composition down. We show that only one rule satisfies irrelevance of null agents, the equal-division lower bound, and our robustness properties. This rule is the uniform rule.