Smith and Rawls Share a Room: Stability and Medians
Abstract
We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the “lonely wolf” theorem and a decomposability result. The latter result together with transitivity of blocking leads to an elementary proof of the so-called stable median matching theorem, showing how the often incompatible concepts of stability (represented by the political economist Adam Smith) and fairness (represented by the political philosopher John Rawls) can be reconciled for roommate problems. Finally, we extend our results to two-sided matching problems.Download Info
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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 009.Length:
Date of creation: 2008
Date of revision:
Handle: RePEc:dgr:umamet:2008009
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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
Related research
Keywords: Economics (Jel: A);Other versions of this item:
- Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer, vol. 35(4), pages 647-667, October.
- Bettina Klaus & Flip Klijn, 2009. "Smith and Rawls Share a Room: Stability and Medians," Harvard Business School Working Papers 09-111, Harvard Business School.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-05-24 (All new papers)
- NEP-CDM-2008-05-24 (Collective Decision-Making)
- NEP-GTH-2008-05-24 (Game Theory)
- NEP-HPE-2008-05-24 (History & Philosophy of Economics)
References
References listed on IDEASPlease 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.:
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- Klaus, Bettina & Klijn, Flip, 2006. "Median stable matching for college admissions," Open Access publications from Maastricht University urn:nbn:nl:ui:27-20032, Maastricht University.
- Bettina Klaus & Flip Klijn, 2004. "Median Stable Matching for College Admission," UFAE and IAE Working Papers 632.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 16 Feb 2006.
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Florian M. Biermann, 2011.
"A Measure to compare Matchings in Marriage Markets,"
Discussion Paper Series
dp575, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Florian M. Biermann, 2011. "A Measure to Compare Matchings in Marriage Markets," Working Papers 2011.41, Fondazione Eni Enrico Mattei.
- Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Working Papers 005-11, International School of Economics at TSU, Tbilisi, Republic of Georgia.
- Bettina Klaus & Flip Klijn & Markus Walzl, 2008.
"Stochastic Stability for Roommate Markets,"
Working Papers
357, Barcelona Graduate School of Economics.
- Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
- Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2008. "Stochastic Stability for Roommate Markets," Research Memoranda 010, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Schwarz, Michael & Yenmez, M. Bumin, 2011. "Median stable matching for markets with wages," Journal of Economic Theory, Elsevier, vol. 146(2), pages 619-637, March.
- Gudmundsson, Jens, 2011. "On symmetry in the formation of stable partnerships," Working Papers 2011:29, Lund University, Department of Economics.
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