How lotteries in school choice help to level the playing field

The use of lotteries is advocated to desegregate schools. We study lottery quotas embedded in the two most common school choice mechanisms, namely deferred and immediate acceptance mechanisms. Some seats are allocated based on merit (e.g., grades) and some based on lottery draws. We focus on the effect of the lottery quota on truth-telling, the utility of students, and the student composition at schools, using theory and experiments. We find that the lottery quota strengthens truth-telling in equilibrium when the deferred acceptance mechanism is used while it has no clear effect on truth-telling in equilibrium for the immediate acceptance mechanism. This finds support in the experiment. Moreover, the lottery quota leads to more diverse school populations in the experiments, as predicted. Comparing the two mechanisms, students with the lowest grades profit more from the introduction of the lottery under immediate than under deferred acceptance.