  A fundamental component in the theoretical school choice literature is the
problem a student faces in deciding which schools to apply to. Recent models
have considered a set of schools of different selectiveness and a student who
is unsure of their strength and can apply to at most $k$ schools. Such models
assume that the student cares solely about maximizing the quality of the school
that they attend, but experience suggests that students' decisions are also
influenced by a set of behavioral biases based on reputational effects: a
subjective reputational benefit when admitted to a selective school, whether or
not they attend; and a subjective loss based on disappointment when rejected.
Guided by these observations, and inspired by recent behavioral economics work
on loss aversion relative to expectations, we propose a behavioral model by
which a student chooses schools to balance these behavioral effects with the
quality of the school they attend.
  Our main results show that a student's choices change in dramatic ways when
these reputation-based behavioral biases are taken into account. In particular,
where a rational applicant spreads their applications evenly, a biased student
applies very sparsely to highly selective schools, such that above a certain
threshold they apply to only an absolute constant number of schools even as
their budget of applications grows to infinity. Consequently, a biased student
underperforms a rational student even when the rational student is restricted
to a sufficiently large upper bound on applications and the biased student can
apply to arbitrarily many. Our analysis shows that the reputation-based model
is rich enough to cover a range of different ways that biased students cope
with fear of rejection, including not just targeting less selective schools,
but also occasionally applying to schools that are too selective, compared to
rational students.
