Methods for Ordinal Peer Grading

Massive Online Open Courses have the potential to revolu-tionize higher education with their wide outreach and acces-sibility, 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 num-ber 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 [5, 38, 29, 9], it is therefore desirable to allow peer graders to make ordinal statements (e.g. ”project X is bet-ter 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 ordi-nal peer grading problem as a type of rank aggregation prob-lem, 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 col-lected 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