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The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier / Wenzelburger, Jan

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

Bettina Klaus
Published Online: 2010-04-09 | DOI: https://doi.org/10.2202/1935-1704.1650

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.

Keywords: fair allocation; single-peaked preferences; population-monotonicity; replacement-domination; replication-invariance

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Published Online: 2010-04-09

Citation Information: The B.E. Journal of Theoretical Economics, Volume 10, Issue 1, ISSN (Online) 1935-1704, DOI: https://doi.org/10.2202/1935-1704.1650.

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