1 Introduction
School choice is referred in the literature on education as giving parents a say in the
choice of the schools their children will attend. A recent paper by Abdulkadiroglu and
Sonmez (2003) has lead to an upsurge of enthusiasm in the use of matching theory for
the design and study of school choice mechanisms.1 Abdulkadiroglu and Sonmez (2003)
discuss critical flaws of the current procedures of some school districts in the US to assign
children to public schools, pointing out that the widely used Boston mechanism has the
serious shortcoming that it is not in the parents’ best interest to reveal their true pref-
erences. Using a mechanism design approach, they propose and analyze two alternative
student assignment mechanisms that do not have this shortcoming: the Student-Optimal
Stable mechanism and the Top Trading Cycles mechanism.
A common practice in real-life school choice situations consists of asking to submit a
preference list containing only a limited number of schools. For instance, in the school
district of New York City each year more than 90,000 students are assigned to about 500
school programs, and parents are asked to submit a preference list containing at most
12 school programs. Until 2006 parents in Boston could not submit more than 5 schools
in their choice list.2 In Spain and in Hungary students applying to a college cannot
submit a choice list containing more than 8 and 4 academic programs, respectively.3 This
restriction is reason for concern. Imposing a curb on the length of the submitted lists
compels participants to adopt a strategic behavior when choosing which ordered list to
submit. For instance, if a participant fears rejection by his most preferred programs, it can
be advantageous not to apply to these programs and use instead its allowed application
slots for less preferred programs.
The matching literature usually assumes that individuals submit their true preferences
when either the Student-Optimal Stable mechanism or the Top Trading Cycles mecha-
1Recent papers include Abdulkadiroglu (2005), Abdulkadiroglu, Pathak, and Roth (2005, 2008), Ab-
dulkadiroglu, Pathak, Roth, and Sonmez (2005), Chen and Sonmez (2006), Erdil and Ergin (2008), Ergin
and Sonmez (2006), Kesten (2005), and Pathak and Sonmez (2008).
2Abdulkadirogglu, Pathak, and Roth (2005) report that in New York about 25% of the students submit
a preference list containing the maximal number of school programs, which suggests that the constraint
is binding for a significant number of students. Interestingly enough, the school district of Boston re-
cently adopted the Student-Optimal Stable mechanism without a constraint on the length of submittable
preference lists for the school year 2007-2008 (see Abdulkadiroglu, Pathak, Roth and Sonmez (2006)).
3In Spain and Hungary colleges are not strategic, for the priority orders are determined by students’
grades. So college admission in these countries is, strictly speaking, akin to school choice.