# The Separability Principle in Economies with Single-Peaked Preferences

- 64 Downloads
- 10 Citations

## Abstract

We investigate the implications of the “separability principle” for the class of problems allocating an infinitely divisible commodity among a group of agents with *single-peaked* preferences. The separability principle requires that for two problems with the same population, but possibly different social endowments, in which the preferences of agents may change, if there is a subgroup of agents whose preferences are the same and the total amounts awarded to them are the same, then the amount awarded to each agent in the subgroup should be the same. First, we investigate the logical relations between *separability* and other axioms. As it turns out, *consistency* implies *separability*. Then, we present characterizations of the *uniform rule* on the basis of *separability* and also on the basis of other axioms.

## Keywords

Econ Theory Pareto Optimality Logical Relation Equal Division Separability Principle## References

- Benassy JP (1982) The economics of market disequilibrium. Academic, San DiegoGoogle Scholar
- Ching S (1992) A simple characterization of the uniform rule. Econ Lett 40:57–60CrossRefGoogle Scholar
- Ching S (1994) An alternative characterization of the uniform rule. Soc Choice Welfare 11:131–136CrossRefGoogle Scholar
- Ching S, Thomson W (1993) Population-monotonic solutions in public good economies with single-peaked preferences, forthcoming. Soc Choice WelfareGoogle Scholar
- Chun Y (1986) The solidarity axiom for quasi-linear social choice problems. Soc Choice Welfare 3:297–320CrossRefGoogle Scholar
- Chun Y (1999) Equivalence of axioms for bankruptcy problems. Int J Game Theory 28:511–520CrossRefGoogle Scholar
- Chun Y (2000) Agreement, separability, and other axioms for quasi-linear social choice problems. Soc Choice Welfare 17:507–521CrossRefGoogle Scholar
- Chun Y (2001) The separability principle in economies with single-peaked preferences. Discussion Paper No. 45, Institute of Economic Research, Seoul National UniversityGoogle Scholar
- Chun Y, Thomson W (1988) Monotonicity properties of bargaining solutions when applied to economics. Math Soc Sci 15:11–27CrossRefGoogle Scholar
- Dagan N (1996) A note on Thomson’s characterizations of the uniform rule. J Econ Theory 69:255–261CrossRefGoogle Scholar
- Ehlers L (2002) Resource-monotonic allocation when preferences are single-peaked. Econ Theory 20:113–131CrossRefGoogle Scholar
- Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7:45–98Google Scholar
- de Frutos MA, Massó J (1995) More on the uniform allocation rule: equality and consistency, mimeoGoogle Scholar
- Herrero C, Villar A (1997) Agenda-independence in allocation problems with single-peaked preferences. University of Alicante and IVIE mimeoGoogle Scholar
- Herrero C, Villar A (2000) An alternative characterization of the equal-distance rule for allocation problems with single-peaked preferences. Econ Lett 66:311–317CrossRefGoogle Scholar
- Klaus B (1998) Fair allocation and reallocation: an axiomatic study. Ph.D Dissertation, University of MaastrichtGoogle Scholar
- Klaus B (2006) A note on the separability principle in economies with single-peaked preferences, mimeo (in press)Google Scholar
- Klaus B, Peters H, Storcken T (1998) Strategy-proof division with single-peaked preferences and individual endowments. Soc Choice Welfare 15:297–311CrossRefGoogle Scholar
- Moulin H (1980) On strategy-proofness and single-peakedness. Public Choice 35:437–455CrossRefGoogle Scholar
- Moulin H (1984) Generalized Condorcet-winners for single-peaked preferences and single- plateau preferences. Soc Choice Welfare 1:127–147CrossRefGoogle Scholar
- Moulin H (1987a) The pure compensation problem: egalitarianism versus laissez-fairism. Q J Econ 102:769–783CrossRefGoogle Scholar
- Moulin H (1987b) Equal or proportional division of a surplus, and other methods. Int J Game Theory 16:161–186CrossRefGoogle Scholar
- Moulin H, Thomson W (1988) Can everyone benefit from growth? Two difficulties. J Math Econ 17:339-345CrossRefGoogle Scholar
- Otten G-J, Peters H, Volij O (1996) Two characterizations of the uniform rule for division problems with single-peaked preferences. Econ Theory 7:291–306Google Scholar
- Roemer J (1986) Equality of resources implies equality of welfare. Q J Econ 101:751–784CrossRefGoogle Scholar
- Schummer J, Thomson W (1997) Two derivations of the uniform rule and an application to bankruptcy. Econ Lett 55:333–337CrossRefGoogle Scholar
- Sönmez T (1994) Consistency, monotonicity, and the uniform rule. Econ Lett 46:229–235CrossRefGoogle Scholar
- Sprumont Y (1991) The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 59:509–519CrossRefGoogle Scholar
- Thomson W (1983a) The fair division of a fixed supply among a growing population. Math Oper Res 8:319–326CrossRefGoogle Scholar
- Thomson W (1983b) Problems of fair division and the egalitarian solution. J Econ Theory 31:211–226CrossRefGoogle Scholar
- Thomson W (1993) The replacement principle in public good economies with single-peaked preferences. Econ Lett 42:31–36CrossRefGoogle Scholar
- Thomson W (1994a) Resource-monotonic solutions to the problem of fair division when preferences are single-peaked. Soc Choice Welfare 11:205–223Google Scholar
- Thomson W (1994b) Consistent solutions to the problem of fair division when preferences are single-peaked. J Econ Theory 63:219–245CrossRefGoogle Scholar
- Thomson W (1995a) Population-monotonic solutions to the problem of fair division when preferences are single-peaked. Econ Theory 5:229–246CrossRefGoogle Scholar
- Thomson W (1995b) Population monotonic allocation rules. In: Barnett WA, Moulin H, Salles M, Schofield NJ (eds) Social choice, welfare, and ethics. Cambridge University Press, Cambridge, pp 79–124Google Scholar
- Thomson W (1997) The replacement principle in economies with single-peaked preferences. J Econ Theory 76:145–168CrossRefGoogle Scholar
- Thomson W (1998a) The replacement principle in economies with indivisible goods. Soc Choice Welfare 15:57–66CrossRefGoogle Scholar
- Thomson W (1998b) Consistency and its converse: an introduction. University of Rochester Working Paper No. 448Google Scholar
- Thomson W (1999) Welfare-domination under preference replacement: a survey and open questions. Soc Choice Welfare 16:373–394CrossRefGoogle Scholar
- Thomson W (2006) The theory of fair allocation. Princton University Press, New Jersey (in press)Google Scholar