Stability is a main concern in the school choice problem. However, it does not come for free. The literature shows that stability is incompatible with Pareto efficiency. Nevertheless, it has been ranked over Pareto efficiency by many school districts, and thereof, they are using stable mechanisms. In this note, we reveal another important cost of stability: ‘‘consistency’’, which is a robustness property that requires from a mechanism that whenever some students leave the problem along with their assignments, the remaining students’ assignments do not change after running the mechanism in the smaller problem. Consequently, we show that no stable mechanism is consistent
