Smith and Rawls Share a Room: Stability and Medians

23 Pages Posted: 2 Apr 2009

See all articles by Bettina-Elisabeth Klaus

Bettina-Elisabeth Klaus

University of Lausanne

Flip Klijn

Autonomous University of Barcelona - Department of Economics and Economic History

Date Written: February 27, 2009

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 "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.

Keywords: fairness, matching, median, stability

JEL Classification: C62, C78

Suggested Citation

Klaus, Bettina-Elisabeth and Klijn, Flip, Smith and Rawls Share a Room: Stability and Medians (February 27, 2009). Harvard Business School NOM Unit Working Paper No. 09-111, Available at SSRN: https://ssrn.com/abstract=1370327 or http://dx.doi.org/10.2139/ssrn.1370327

Bettina-Elisabeth Klaus (Contact Author)

University of Lausanne ( email )

Quartier Chambronne
Lausanne, Vaud CH-1015
Switzerland

Flip Klijn

Autonomous University of Barcelona - Department of Economics and Economic History ( email )

Edifici B - Campus Bellaterra
Barcelona, 08193
Spain

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