Abstract
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 Ω-continuity. We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of Ω-continuity. Furthermore, we prove that the 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, the equal division lower bound, separability, and either Ω-continuity or duplication-invariance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benassy JP (1982) The economics of market equilibrium. Academic Press, San Diego
Ching S (1992) A simple characterization of the uniform rule. Econ Lett 40:57–60
Ching S (1994) An alternative characterization of the uniform rule. Soc Choice Welfare 11:131–136
Chun Y (1999) Equivalence of axioms for bankruptcy problems. Int J Game Theory 28:511–520
Chun Y (2000) Agreement, separability, and other axioms for quasi-linear social choice problems. Soc Choice Welfare 17:507–521
Chun Y (2003) One-sided population monotonicity, separability, and the uniform rule. Econ Lett 78:343–349
Chun Y (2006) The separability principle in economies with single-peaked preferences. Soc Choice Welfare (forthcoming)
Dagan N (1996) A note on Thomson’s characterizations of the uniform rule. J Econ Theory 69:255–261
Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7:45–98
Klaus B (1998) Fair allocation and reallocation: an axiomatic study. Ph.D Thesis, Maastricht University
Moulin H (1987) Equal or proportional division of a surplus, and other methods. Int J Game Theory 16:161–186
Sönmez T (1994) Consistency, monotonicity, and the uniform rule. Econ Lett 46:229–235
Sprumont Y (1991) The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 59:509–519
Thomson W (1994a) Consistent solutions to the problem of fair division when preferences are single-peaked. J Econ Theory 63:219–245
Thomson W (1994b) Resource-monotonic solutions to the problem of fair division when preferences are single-peaked. Soc Choice Welfare 11:205–223
Thomson W (1995) Population-monotonic solutions to the problem of fair division when preferences are single-peaked. Econ Theory 5:229–246
Thomson W (1997) The replacement principle in economies with single-peaked preferences. J Econ Theory 76:145–168
Thomson W (2006) The theory of fair allocation. Princeton University Press (forthcoming)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Klaus, B. A Note on the Separability Principle in Economies with Single-Peaked Preferences. Soc Choice Welfare 26, 255–261 (2006). https://doi.org/10.1007/s00355-006-0096-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-006-0096-0