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Uniform allocation and reallocation revisited.

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F:REDBD6-1RED031 Rev. Econ. Design 6, 85–98 (2001) c© Springer-Verlag 2001 Uniform allocation and reallocation revisited Bettina Klaus Department of Economics, University of Nebraska at Lincoln, Lincoln, NE 68588-0489, USA (e-mail: [email protected]) Received: 20 February 1999 / Accepted: 15 February 2000 Abstract. Thomson (1995a) proved that the uniform allocation rule is the only allocation rule for allocation economies with single-peaked preferences that satisfies Pareto efficiency, no-envy, one-sided population-monotonicity, and replication-invariance on a restricted domain of single-peaked preferences. We prove that this result also holds on the unrestricted domain of single-peaked preferences. Next, replacing one-sided population-monotonicity by one-sided replacement- domination yields another characterization of the uniform allocation rule, Thom- son (1997a). We show how this result can be extended to the more general frame- work of reallocation economies with individual endowments and single-peaked preferences. Following Thomson (1995b) we present allocation and reallocation economies in a unified framework of open economies. JEL classification: D63, D71 Key words: Fair allocation and reallocation, open economies, single-peaked pref- erences, population-monotonicity, replacement-domination 1 Introduction We consider the allocation of some perfectly divisible commodity in economies with single-peaked preferences. Typical examples can be derived from rationing (Benassy 1982) or from simple resource allocation problems; for instance the Part of this paper was written while the author was visiting the University of Rochester. I acknowledge the hospitality of the Department of Economics at the University of Rochester and the financial support of the Netherlands Organization for Scientific Research (NWO). I wish to thank William Thomson, Gabrielle Demange, and the referees for many helpful comments. 86 B. Klaus allocation of a task among the members of a team. In

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