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...

In priority-based two-sided matchings, a respecting-improvements property of a mechanism requires that an agent should get weakly better off when she is assigned a higher priority. Not only is it a normative desideratum, it is also important for ex-ante investments and for disclosure of...