Respecting Priorities when Assigning Students to Schools

We consider the problem of assigning students to schools on the basis of priorities. Students are allowed to have equal priority at a school. We characterize the efficient rules which weakly/strongly respect students’ priorities. When priority orderings are not strict, it is not possible to simply break ties in a fixed manner. All possibilities of resolving the indifferences need to be considered. Neither the deferred acceptance algorithm nor the top trading cycle algorithm successfully solve the problem of efficiently assigning the students to schools whereas a modified version of the deferred acceptance algorithm might. In this version tie breaking depends on students’ preferences.