  We study the role of information and access in capacity-constrained selection
problems with fairness concerns. We develop a theoretical statistical
discrimination framework, where each applicant has multiple features and is
potentially strategic. The model formalizes the trade-off between the
(potentially positive) informational role of a feature and its (negative)
exclusionary nature when members of different social groups have unequal access
to this feature.
  Our framework finds a natural application to recent policy debates on
dropping standardized testing in college admissions. Our primary takeaway is
that the decision to drop a feature (such as test scores) cannot be made
without the joint context of the information provided by other features and how
the requirement affects the applicant pool composition. Dropping a feature may
exacerbate disparities by decreasing the amount of information available for
each applicant, especially those from non-traditional backgrounds. However, in
the presence of access barriers to a feature, the interaction between the
informational environment and the effect of access barriers on the applicant
pool size becomes highly complex. In this case, we provide a threshold
characterization regarding when removing a feature improves both academic merit
and diversity. Finally, using calibrated simulations in both the strategic and
non-strategic settings, we demonstrate the presence of practical instances
where the decision to eliminate standardized testing improves or worsens all
metrics.
