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The Role of Replication-Invariance: Two Answers Concerning the Problem of Fair Division When Preferences Are Single-Peaked

  • Klaus Bettina

    ()

    (University of Lausanne)

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.

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Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

Volume (Year): 10 (2010)
Issue (Month): 1 (April)
Pages: 1-14

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Handle: RePEc:bpj:bejtec:v:10:y:2010:i:1:n:14
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