Gender consistent resolving rules in marriage problems

The selection of blocking pairs to be matched plays an important role in the study of mechanisms converting arbitrary matchings into stable ones. We assume that a resolving rule guides the selection and show that two axioms (independence and top optimality) transform such a rule into a gender consistent one. That is, the rule is forced by the axioms to follow a linear order over acceptable pairs which is consistent with the preferences of either all men or all women. As shown by Abeledo and Rothblum (1995), stable matchings can be reached when starting from an arbitrary individually rational matching and iteratively satisfying the pair selected by a gender consistent resolving rule.