Correlation Neglect in Student-to-School Matching, by Rees-Jones, Shorrer, and Tergiman

Suppose it is costly to apply to schools (perhaps because you are only allowed n applications, and have a larger set of schools you are interested in.)  Now suppose that your first choice is Yale and your second is Harvard. Should you apply to both?  How about if it is the case that, if Yale rejects you, Harvard probably will too?  That turns out to be harder for many people to figure out than you might think...

Correlation Neglect in Student-to-School Matching
Alex Rees-Jones, Ran I. Shorrer, and Chloe Tergiman

Abstract
A growing body of evidence suggests that decision-makers fail to account for correlation in signals that they receive. We study the relevance of this mistake in students' interactions with school- choice matching mechanisms. In a lab experiment presenting simple and incentivized school-choice scenarios, we find that subjects tend to follow optimal application strategies when schools' admissions decisions are determined independently. However, when schools rely on a common priority — inducing correlation in their decisions — decision making suffers: application strategies become substantially more aggressive and fail to include attractive "safety" options. We document that this pattern holds even within-subject, with significant fractions of participants applying to different programs in mathematically equivalent situations that differ only by the presence of correlation. We provide a battery of tests suggesting that this phenomenon is at least partially driven by correlation neglect, and we discuss implications that arise for the design and deployment of student-to-school matching mechanisms.