Equal opportunities in many-to-one matching markets

We introduce a notion of fairness, inspired by the equality of opportunity literature, into many-to-one matching markets endowed with a measure of the quality of a match between two entities in the market. In this framework, fairness considerations are made by a social evaluator based on the match quality distribution. We impose the standard notion of stability as minimal desideratum and study matching that satisfy our notion of fairness and a notion of efficiency based on aggregate match quality. To overcome some of the identified incompatibilities, we propose two alternative approaches. The first one is a linear programming solution to maximize fairness under stability constraints. The second approach weakens fairness and efficiency to define a class of opportunity egalitarian social welfare functions that evaluate stable matchings. We then describe an algorithm to find the stable matching that maximizes social welfare.