Modeling reputation-based behavioral biases in school choice

Abstract

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.

Figures (8)

• Figure 1: As shown here, a biased student in our model concentrates most of their applications on less selective schools, and applies very sparsely to the more selective end of the range. The plot shows the positions (on the interval $[0,1]$) of $k = 100$ applications sent out by a student with bias parameter $\gamma = 0.1$.
• Figure 2: Expected (biased) utility $U_\gamma(x)$ for a student applying to a single school $x$.
• Figure 3: A plot of $\Delta_i$ for $\leq i \leq 25$ in an optimal biased portfolio for $k=25$ and $\gamma=0.1$.
• Figure 4: A plot of the function $h(\gamma)$ such that for any $k$, $x_2\leq h(\gamma)$.
• Figure 5: A bound on the number of schools above $c$ that a student applies to as a function of $c$.

Theorems & Definitions (30)

• Proposition 4.1
• proof
• Corollary 4.2
• proof
• Proposition 4.4
• proof
• Proposition 5.1
• proof
• Corollary 5.2
• Proposition 5.3