Stable Partitions in Many Division Problems: The Proportional and the Sequential Dictator Solutions
We study how to partition a set of agents in a stable way when each coalition in the partition has to share a unit of a perfectly divisible good, and each agent has symmetric single-peaked preferences on the unit interval of his potential shares. A rule on the set of preference profiles consists of a partition function and a solution. Given a preference profile, a partition is selected and as many units of the good as the number of coalitions in the partition are allocated, where each unit is shared among all agents belonging to the same coalition according to the solution. A rule is stable at a preference profile if no agent strictly prefers to leave his coalition to join another coalition and all members of the receiving coalition want to admit him. We show that the proportional solution and all sequential dictator solutions admit stable partition functions. We also show that stability is a strong requirement that becomes easily incompatible with other desirable properties like e¢ ciency, strategy-proofness, anonymity, and non-envyness.
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- Jordi Massó & Inés Moreno de Barreda, 2010.
"On Strategy-proofness and Symmetric Single-peakedness,"
UFAE and IAE Working Papers
809.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Massó, Jordi & Moreno de Barreda, Inés, 2011. "On strategy-proofness and symmetric single-peakedness," Games and Economic Behavior, Elsevier, vol. 72(2), pages 467-484, June.
- Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
- Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
- EHLERS, Lars, 2001.
"On Fixed-Path Rationing Methods,"
Cahiers de recherche
2001-24, Universite de Montreal, Departement de sciences economiques.
- Anirban Kar & Özgür Kıbrıs, 2008. "Allocating multiple estates among agents with single-peaked preferences," Social Choice and Welfare, Springer, vol. 31(4), pages 641-666, December.
- Schummer, James & Thomson, William, 1997.
"Two derivations of the uniform rule and an application to bankruptcy,"
Elsevier, vol. 55(3), pages 333-337, September.
- Schummer, J. & Thomson, W., 1996. "Two Derivations of the Uniform Rule and an Application to Bankruptcy," RCER Working Papers 423, University of Rochester - Center for Economic Research (RCER).
- Lars Ehlers, 2002. "Resource-monotonic allocation when preferences are single-peaked," Economic Theory, Springer, vol. 20(1), pages 113-131.
- Herrero, Carmen & Villar, Antonio, 2000. "An alternative characterization of the equal-distance rule for allocation problems with single-peaked preferences," Economics Letters, Elsevier, vol. 66(3), pages 311-317, March.
- Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
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