The Role of Replication-Invariance: Two answers Concerning the Problem of Fair Division when Preferences are Single-Peaked

B.E. Klaus

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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 (1995b) 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.
Original languageEnglish
Number of pages14
JournalThe B.E. Journal of Theoretical Economics
Issue number1
Publication statusPublished - 1 Jan 2010

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