, Volume 8, Issue 3, pp 249-268

Probabilistic assignments of identical indivisible objects and uniform probabilistic rules

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Abstract.

We consider a probabilistic approach to the problem of assigning k indivisible identical objects to a set of agents with single-peaked preferences. Using the ordinal extension of preferences we characterize the class of uniform probabilistic rules by Pareto efficiency, strategy-proofness, and no-envy. We also show that in this characterization no-envy cannot be replaced by anonymity. When agents are strictly risk averse von Neumann-Morgenstern utility maximizer, then we reduce the problem of assigning k identical objects to a problem of allocating the amount k of an infinitely divisible commodity.

Received: 1 January 2002, Accepted: 5 February 2003,

JEL Classification:

D63, D71, D81

Bettina Klaus: B. Klaus is supported by a Ramón y Cajal contract and by Research Grant BEC 2002-02130 from the Spanish Ministerio de Ciencia y Tecnología.
The authors thank William Thomson for many helpful comments.