  Due to the Covid-19 pandemic, more than 500 US-based colleges and
universities went "test-optional" for admissions and promised that they would
not penalize applicants for not submitting test scores, part of a longer trend
to rethink the role of testing in college admissions. However, it remains
unclear how (and whether) a college can simultaneously use test scores for
those who submit them, while not penalizing those who do not--and what that
promise even means. We formalize these questions, and study how a college can
overcome two challenges with optional testing: $\textit{strategic applicants}$
(when those with low test scores can pretend to not have taken the test), and
$\textit{informational gaps}$ (it has more information on those who submit a
test score than those who do not). We find that colleges can indeed do so, if
and only if they are able to use information on who has test access and are
willing to randomize admissions.
