A Note on the Separability Principle in Economies with Single-Peaked
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 analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and continuity (with respect to the social endowment). We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of continuity. Furthermore, we prove that Pareto optimality, equal division lower bound, and separability imply no-envy. Using this result, we strengthen one of Chun's (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, equal division lower bound, separability, and either continuity or duplication-invariance.
|Date of creation:||14 Jan 2004|
|Date of revision:||14 Nov 2005|
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- Thomson, William, 1995.
"Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked,"
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- Thomson, W., 1991. "Population-Monotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked," RCER Working Papers 302, University of Rochester - Center for Economic Research (RCER).
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- Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
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