We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the previous analysis of the problem is the so-called uniform rule. Thomson (1995a) proved that the uniform rule is the only rule satisfying Pareto optimality, no-envy, one-sided population-monotonicity, and replication-invariance. Replacing one-sided population-monotonicity by one-sided replacement-domination} yields another characterization of the uniform rule (Thomson, 1997a). Until now, the independence of replication-invariance from the other properties in these characterizations was an open problem. In this note we prove this independence by means of a single example.
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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number
029.