Ex-ante fairness in the Boston and serial dictatorship mechanisms under pre-exam and post-exam preference submission

In a school choice mechanism, school priorities are often based on student exam scores, by which student true ability may not be perfectly revealed. An ex-post fair matching mechanism (for example, Serial Dictatorship) can be undesirable in that it is not ex-ante fair: it may not match students with higher abilities to better schools, although it always matches students with higher scores to better schools. In this paper we consider a potential way of improving ex-ante fairness - a Boston mechanism with the requirement that students submit their preferences before the exam score is realized (the “pre-BOS mechanism”). This mechanism is more likely to achieve complete ex-ante fairness, in that students with higher ability are always matched with better schools. However, the other mechanisms (pre-/post-SD and post-BOS) can always implement stochastic ex-ante fairness (students with higher ability having higher probability of admission to better schools), while pre-BOS may not.