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 "lone 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.
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Bibliographic InfoPaper provided by Harvard Business School in its series Harvard Business School Working Papers with number 09-111.
Length: 23 pages
Date of creation: Feb 2009
Date of revision:
fairness; matching; median; stability.;
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.
- 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).
- 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-2009-04-05 (All new papers)
- NEP-CDM-2009-04-05 (Collective Decision-Making)
- NEP-GTH-2009-04-05 (Game Theory)
- NEP-HPE-2009-04-05 (History & Philosophy of Economics)
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