  MOOCs have the potential to revolutionize higher education with their wide
outreach and accessibility, but they require instructors to come up with
scalable alternates to traditional student evaluation. Peer grading -- having
students assess each other -- is a promising approach to tackling the problem
of evaluation at scale, since the number of "graders" naturally scales with the
number of students. However, students are not trained in grading, which means
that one cannot expect the same level of grading skills as in traditional
settings. Drawing on broad evidence that ordinal feedback is easier to provide
and more reliable than cardinal feedback, it is therefore desirable to allow
peer graders to make ordinal statements (e.g. "project X is better than project
Y") and not require them to make cardinal statements (e.g. "project X is a
B-"). Thus, in this paper we study the problem of automatically inferring
student grades from ordinal peer feedback, as opposed to existing methods that
require cardinal peer feedback. We formulate the ordinal peer grading problem
as a type of rank aggregation problem, and explore several probabilistic models
under which to estimate student grades and grader reliability. We study the
applicability of these methods using peer grading data collected from a real
class -- with instructor and TA grades as a baseline -- and demonstrate the
efficacy of ordinal feedback techniques in comparison to existing cardinal peer
grading methods. Finally, we compare these peer-grading techniques to
traditional evaluation techniques.
