Multiple Levels of Importance in Matching with Distributional Constraints

In this paper, we study the two-sided matching problem with soft diversity constraints in which each student belongs to one type and each school imposes soft targets on each type. We first identify limitations of type-specific quotas in a previous model and introduce a new general model that takes different levels of importance of types into account. Then we propose a new algorithm that yields a non-wasteful and fair outcome with respect to different levels of importance.