Smith and Rawls share a room: stability and medians
AbstractWe 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 âlonely wolfâ 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.
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Bibliographic InfoArticle provided by Springer in its journal Social Choice and Welfare.
Volume (Year): 35 (2010)
Issue (Month): 4 (October)
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Web page: http://link.springer.de/link/service/journals/00355/index.htm
Other versions of this item:
- Klaus, Bettina & Klijn, Flip, 2008. "Smith and Rawls Share a Room: Stability and Medians," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- 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
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- Jackson, Matthew O. & Watts, Alison, 2002.
"The Evolution of Social and Economic Networks,"
Journal of Economic Theory,
Elsevier, vol. 106(2), pages 265-295, October.
- Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
- Effrosyni Diamantoudi & Eiichi Miyagawa & Licun Xue, 2002.
"Random paths to stability in the roommate problem,"
0102-65, Columbia University, Department of Economics.
- Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May.
- Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
- Bettina Klaus & Flip Klijn, 2006.
"Median Stable Matching for College Admissions,"
International Journal of Game Theory,
Springer, vol. 34(1), pages 1-11, April.
- Bettina Klaus & Flip Klijn, 2004. "Median Stable Matching for College Admission," Working Papers 165, Barcelona Graduate School of Economics.
- 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.
- Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
- Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
- Gudmundsson, Jens, 2011. "On symmetry in the formation of stable partnerships," Working Papers 2011:29, Lund University, Department of Economics.
- Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2014. "The Roommate Problem - Is More Stable Than You Think," CESifo Working Paper Series 4676, CESifo Group Munich.
- Florian M. Biermann, 2011.
"A Measure to Compare Matchings in Marriage Markets,"
2011.41, Fondazione Eni Enrico Mattei.
- 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 005-11, International School of Economics at TSU, Tbilisi, Republic of Georgia.
- Boudreau, James W. & Knoblauch, Vicki, 2014. "What price stability? Social welfare in matching markets," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 27-33.
- Bettina Klaus & Flip Klijn & Markus Walzl, 2008.
"Stochastic Stability for Roommate Markets,"
357, Barcelona Graduate School of Economics.
- James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
- 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.
- Burak Can & Bettina Klaus, 2013.
"Consistency and population sensitivity properties in marriage and roommate markets,"
Social Choice and Welfare,
Springer, vol. 41(4), pages 835-862, October.
- Burak Can & Bettina Klaus, 2010. "Consistency and Population Sensitivity Properties in Marriage and Roommate Markets," Cahiers de Recherches Economiques du DÃ©partement d'EconomÃ©trie et d'Economie politique (DEEP) 10.08, Université de Lausanne, Faculté des HEC, DEEP.
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