Population-monotonicity and separability for economies with single-dipped preferences and the assignment of an indivisible object
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We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. We consider rules that satisfy Pareto efficiency, strategy-proofness, and in addition either the consistency property separability or the solidarity property population-monotonicity. We show that the class of rules that satisfy Pareto efficiency, strategy-proofness, and separability equals the class of rules that satisfy Pareto efficiency, strategy-proofness, and non-bossiness. We also provide characterizations of all rules satisfying Pareto efficiency, strategy-proofness, and either separability or population-monotonicity. Since any such rule consists for the largest part of serial-dictatorship components, we can interpret the characterizations as impossibility results.
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