Stable Mechanisms in Controlled School Choice

We consider a controlled school choice model where students are divided into several types such as socioeconomically advantaged and disadvantaged. The priority for a school is dependent on the type distribution of the assignment. Our model is a generalization of several models in previous studies such as those in which the priorities are based on type quotas and/or reserves. We consider the case where the priority for each school is represented by a weak order and introduce a stable and group strategy-proof mechanism. Moreover, if the priority order for each school is restricted to be a strict order, then the mechanism is also a student optimal stable one. We generalize the model allowing that the priority orders for some schools are not weak, but partial. In this case, a stable mechanism is also introduced.