All About Priorities: Is There School Choice in the Presence of Bad Schools?
When school choice is implemented it is often implied that parents preferences will determine the school their children attend. The matching literature in school choice shows how the design of the norms that govern the allocation process can have different desirable properties but that no unique mechanism has them all. The literature has ignored a crucial aspect in this process, which is the importance of the priorities that the administration give for the different schools in determining the final allocation. We show that if all individuals agree on what the worse schools are, the two most debated mechanisms, the Boston mechanism and the Gale Shapley, will provide an allocation that fully corresponds to those priorities independently of families' listed preferences. Top Trading Cycles, a third proposal presented in the literature but not implemented yet, improves upon the allocation determined by priorities and therefore is the only responding to parents preferences. Another interpretation of the results is that if the authorities have some preferences over where families should go to school they can implement them fully through setting priorities accordingly and choosing the Boston or GS mechanisms, which are the two most commonly used mechanisms.