We consider the problem of allocating a single infinitely divisible commodity to agents with single-peaked preferences, and establish two properties of the rule that has played the central role in the analysis of this problem, the uniform role. Among the efficient allocations, it selects (1) the...

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is "lifted" if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number...