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...

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...

We consider school choice when the priority of a student for a school is conditional on who the other students are. Students have one of several types and the type distribution in the school matters. As a special class of our priority rules, we introduce the adjusted scoring rules and show that...