Smith and Rawls share a room: stability and medians
 Bettina Klaus,
 Flip Klijn
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
We consider onetoone, onesided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a socalled bichoice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the “lone wolf” theorem and a decomposability result. The latter result together with transitivity of blocking leads to an elementary proof of the socalled 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 twosided matching problems.
 Chung, KS (2000) On the existence of stable roommate matchings. Games Econ Behav 33: pp. 206230 CrossRef
 Diamantoudi, E, Miyagawa, E, Xue, L (2004) Random paths to stability in the roommate problem. Games Econ Behav 48: pp. 1828 CrossRef
 Fleiner T (2002) Some results on stable matchings and fixed points. Technical Report TR200208, Egerváry Research Group, Budapest. http://www.cs.elte.hu/egres
 Gale, D, Shapley, LS (1962) College admissions and the stability of marriage. Am Math Mon 69: pp. 915 CrossRef
 Gusfield, D, Irving, RW (1989) The stable marriage problem: structure and algorithms. The MIT Press, Cambridge
 Jackson, MO, Watts, A (2002) The evolution of social and economic networks. J Econ Theory 106: pp. 265295 CrossRef
 Klaus, B, Klijn, F (2006) Median stable matching for college admissions. Int J Game Theory 34: pp. 111 CrossRef
 Knuth, DE (1976) Marriages stables. Les Presses de l’Université de Montreal, Montreal
 Martínez, R, Massó, J, Neme, A, Oviedo, J (2000) Single agents and the set of manytoone stable matchings. J Econ Theory 91: pp. 91105 CrossRef
 McVitie, DG, Wilson, LB (1970) Stable marriage assignments for unequal sets. BIT 10: pp. 295309 CrossRef
 Rawls, J (1971) A theory of justice. Harvard University Press, Cambridge
 Roth, AE (1984) The evolution of the labor market for medical interns and residents: a case study in game theory. J Political Econ 92: pp. 9911016 CrossRef
 Roth, AE (1985) The college admissions problem is not equivalent to the marriage problem. J Econ Theory 36: pp. 277288 CrossRef
 Roth, AE (1986) On the allocation of residents to rural hospitals: a general property of twosided matching markets. Econometrica 54: pp. 425428 CrossRef
 Roth, AE, Sotomayor, MAO (1989) The college admissions problem revisited. Econometrica 57: pp. 559570 CrossRef
 Roth, AE, Sotomayor, MAO (1990) Twosided matching: a study in gametheoretic modeling and analysis. Cambridge University Press, Cambridge
 Sethuraman, J, Teo, CP (2001) A polynomialtime algorithm for the bistable roommates problem. J Comput Syst Sci 63: pp. 486497 CrossRef
 Sethuraman, J, Teo, CP, Qian, L (2006) Manytoone stable matching: geometry and fairness. Math Oper Res 31: pp. 581596 CrossRef
 Tan, J (1991) A necessary and sufficient condition for the existence of a complete stable matching. J Algorithms 12: pp. 154178 CrossRef
 Teo, CP, Sethuraman, J (1998) The geometry of fractional stable matchings and its applications. Math Oper Res 23: pp. 874891 CrossRef
 Yenmez MB, Schwarz M (2009) Median stable matching for markets with wages. Mimeo
 Title
 Smith and Rawls share a room: stability and medians
 Journal

Social Choice and Welfare
Volume 35, Issue 4 , pp 647667
 Cover Date
 20101001
 DOI
 10.1007/s0035501004558
 Print ISSN
 01761714
 Online ISSN
 1432217X
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Bettina Klaus ^{(1)}
 Flip Klijn ^{(2)}
 Author Affiliations

 1. Faculty of Business and Economics, University of Lausanne, Internef 538, 1015, Lausanne, Switzerland
 2. Institute for Economic Analysis (CSIC), Campus UAB, 08193, Bellaterra (Barcelona), Spain