18 research outputs found
Smith and Rawls share a room: stability and medians
El pdf del artículo es el documento de trabajo.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.Plan Nacional I+D+i (ECO2008–04784), Generalitat
de Catalunya (SGR2009–01142), the Barcelona GSE Research Network, and the Consolider-Ingenio 2010
(CSD2006–00016) program