Sigal Oren

A fundamental component in the growing theoretical literature on school choice is the problem a student faces in deciding which schools to apply to. Recent models have considered a setting with a set of schools of different selectiveness, and a student who is unsure of their strength as an applicant and can apply to at most k schools [Ali and Shorrer, 2023]. Such models assume that the student cares solely about maximizing the quality of the school that they will attend. However, experience suggests that students' decisions are additionally influenced by a set of crucial behavioral biases based on reputational effects: they experience a subjective reputational benefit when they are admitted to a selective school, whether or not they attend; and a subjective loss based on disappointment when they are rejected. Guided by these observations, and inspired by recent behavioral economics work on loss aversion relative to expectations [Dreyfuss et al., 2022, Kőszegi and Rabin, 2006, 2007, 2009, Meisner and von Wangenheim, 2023], we propose a behavioral model by which a student chooses schools in a way that balances these subjective behavioral effects with the quality of the school they eventually attend.
Our main results show that a student's choices change in interesting and dramatic ways in a model where these reputation-based behavioral biases are taken into account. In particular, where a rational applicant spreads their applications evenly across the spectrum of school selectiveness at optimality, 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 available 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 through their application decisions, including not just targeting less selective schools, but also occasionally applying to schools that are too selective, compared to rational students.