School choice with preference rank classes

We introduce and study a large family of rules for many-to-one matching problems, the Preference Rank Partitioned (PRP) rules. PRP are student-proposing Deferred Acceptance rules, where schools select among applicants in each round taking into account both students' preferences schools' priorities. In rule school first seeks to students based on priority rank classes, subsequently preference classes. include many well-known such as classic rule, Boston Chinese Application-Rejection Chen Kesten (2017), French Priority Bonkoungou (2020), addition that have not been studied yet. analyze stability, efficiency incentive properties this unified framework.