How Lotteries in School Choice Help Leveling the Playing Field
To reduce segregation and unequal educational opportunities, the city of Berlin introduced
a new admission procedure in the academic year 2010/2011. Schools are no longer
allowed to use geographic proximity as an admission criterion. Moreover, in the case
of oversubscription, they can assign at most 60% of their seats based on applicants'
academic attainment and have to assign 30% via a lottery, with the remaining 10%
reserved for cases of hardship.1 Both the role and the size of this lottery quota were
highly controversial. Left-leaning politicians who favoured a less di erentiated student
composition across schools (and hence a more diverse student composition within
schools) called for a larger lottery quota,2 while right-leaning politicians criticized a
lottery as arbitrary and favoured academic attainment as the principal determinant for
priorities.3
Besides the use of a lottery, the Berlin mechanism is also controversial in that it
applies an immediate acceptance algorithm. This algorithm has been widely used in
many cities, most notably in Boston, where it rst attracted the interest of economists.
Following protests of parents and after the involvement of economists helping with the
design of a new mechanism, Boston abandoned its immediate acceptance mechanism in
2005. The main criticism was that under the immediate acceptance mechanism parents
have to manipulate their rank-order lists over schools to achieve a good outcome.4 Such
manipulations require strategic sophistication and information about the demand for the
schools.5 Thus, the mechanism favors better-informed parents over others. Under the
new mechanism that is based on the deferred acceptance algorithm, parents cannot gain
from misrepresenting their true preferences. This property, called strategy-proofness,
levels the playing eld among the parents. Moreover, truthful reports can serve as
a valuable feedback to school authorities on the quality of and the true demand for
particular schools.
In this paper, we use theory and experiments to understand the properties of the
existing mechanism in Berlin, and more generally, to understand the influence of a
lottery on the two most frequently applied matching mechanisms, the immediate and
the deferred acceptance mechanism. Speci cally, following up on the controversies
around the lottery and taking into account the criticism of the immediate acceptance
mechanism, we seek to understand whether the mechanism achieves the political goals
of a more diverse student composition in schools and hence less segregation. In addition,
we investigate an alternative mechanism with a lottery that is based on the deferred
acceptance algorithm. We show how a lottery quota combined with the deferred
acceptance mechanism levels the playing eld in two ways: (i) it gives students with
a low priority a chance to get a seat at their preferred school and, additionally, (ii) it
reinforces the strategy-proofness of the deferred acceptance mechanism by making it
strictly dominant for more students to report their true preferences.