Stable Partitions in Many Division Problems: The Proportional and the Sequential Dictator Solutions
AbstractWe 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 efficiency, strategy-proofness, anonymity, and non-envyness.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Barcelona Graduate School of Economics in its series Working Papers with number 739.
Date of creation: Oct 2013
Date of revision:
division problem; symmetric single-peaked preferences; stable partition;
Other versions of this item:
- Gustavo Bergantiños & Jordi Massó & Inés Moreno de Barreda & Alejandro Neme, 2013. "Stable Partitions in Many Division Problems: The Proportional and the Sequential Dictator Solutions," UFAE and IAE Working Papers 941.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-12-20 (All new papers)
- NEP-CDM-2013-12-20 (Collective Decision-Making)
- NEP-GTH-2013-12-20 (Game Theory)
- NEP-HPE-2013-12-20 (History & Philosophy of Economics)
- NEP-MIC-2013-12-20 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ehlers, L., 2001.
"On Fixed-Path Rationing Methods,"
Cahiers de recherche
2001-24, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- 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.
- 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, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
- 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.
- Lars Ehlers, 2002. "Resource-monotonic allocation when preferences are single-peaked," Economic Theory, Springer, vol. 20(1), pages 113-131.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bruno Guallar).
If references are entirely missing, you can add them using this form.