We propose the PeerRank method for peer assessment. This constructs a grade for an agent based on the grades proposed by the agents evaluating the agent. Since the grade of an agent is a measure of their ability to grade correctly, the PeerRank method weights grades by the grades of the grading agent. The PeerRank method also provides an incentive for agents to grade correctly. As the grades of an agent depend on the grades of the grading agents, and as these grades themselves depend on the grades of other agents, we define the PeerRank method by a fixed point equation similar to the PageRank method for ranking web-pages. We identify some formal properties of the PeerRank method (for example, it satisfies axioms of unanimity, no dummy, no discrimination and symmetry), discuss some examples, compare with related work and evaluate the performance on some synthetic data. Our results show considerable promise, reducing the error in grade predictions by a factor of 2 or more in many cases over the natural baseline of averaging peer grades.
Another work which is close to ours is the CrowdGrader mechanism for peer evaluation from UC Santa Cruz @cite_8 . CrowdGrader lets students submit and collaboratively grade solutions to homework assignments. The tool permitted both ranking and grading of homework. However, de Alfaro and Shavlovsky found that students much preferred to grade than to rank. They expressed uneasiness in ranking their peers, perceiving ranking as a blunt tool compared to grading. At the heart of CrowdGrader is the Vancouver algorithm for combining peer grades. In each iteration, this algorithm computes a consensus estimate of the grade of each submission, weighing grades according to the (estimated) accuracy of each student; the consensus estimates are then used to update the estimated accuracy of the students. The update attempts to minimize variance.
@cite_8
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Crowdsourcing offers a practical method for ranking and scoring large amounts of items. To investigate the algorithms and incentives that can be used in crowdsourcing quality evaluations, we built CrowdGrader, a tool that lets students submit and collaboratively grade solutions to homework assignments. We present the algorithms and techniques used in CrowdGrader, and we describe our results and experience in using the tool for several computer-science assignments. CrowdGrader combines the student-provided grades into a consensus grade for each submission using a novel crowdsourcing algorithm that relies on a reputation system. The algorithm iterativerly refines inter-dependent estimates of the consensus grades, and of the grading accuracy of each student. On synthetic data, the algorithm performs better than alternatives not based on reputation. On our preliminary experimental data, the performance seems dependent on the nature of review errors, with errors that can be ascribed to the reviewer being more tractable than those arising from random external events. To provide an incentive for reviewers, the grade each student receives in an assignment is a combination of the consensus grade received by their submissions, and of a reviewing grade capturing their reviewing effort and accuracy. This incentive worked well in practice. CrowdGrader is a system that lets students submit and collaboratively review and grade homework. We describe the techniques and ideas used in CrowdGrader, and report on the experience of using CrowdGrader in disciplines ranging from Computer Science to Economics, Writing, and Technology. In CrowdGrader, students receive an overall crowd-grade that reflects both the quality of their homework, and the quality of their work as reviewers. This creates an incentive for students to provide accurate grades and helpful reviews of other students' work. Instructors can use the crowd-grades as final grades, or fine-tune the grades according to their wishes. Our results on seven classes show that students actively participate in the grading and write reviews that are generally helpful to the submissions' authors. The results also show that grades computed by CrowdGrader are sufficiently precise to be used as the homework component of class grades. Students report that the main benefits in using CrowdGrader are the quality of the reviews they receive, and the ability to learn from reviewing their peers' work. Instructors can leverage peer learning in their classes, and easily handle homework evaluation in large classes. In massive open online courses (MOOCs), peer grading serves as a critical tool for scaling the grading of complex, open-ended assignments to courses with tens or hundreds of thousands of students. But despite promising initial trials, it does not always deliver accurate results compared to human experts. In this paper, we develop algorithms for estimating and correcting for grader biases and reliabilities, showing significant improvement in peer grading accuracy on real data with 63,199 peer grades from Coursera's HCI course offerings --- the largest peer grading networks analysed to date. We relate grader biases and reliabilities to other student factors such as student engagement, performance as well as commenting style. We also show that our model can lead to more intelligent assignment of graders to gradees. Peer and self-assessment offer an opportunity to scale both assessment and learning to global classrooms. This article reports our experiences with two iterations of the first large online class to use peer and self-assessment. In this class, peer grades correlated highly with staff-assigned grades. The second iteration had 42.9p of students’ grades within 5p of the staff grade, and 65.5p within 10p. On average, students assessed their work 7p higher than staff did. Students also rated peers’ work from their own country 3.6p higher than those from elsewhere. We performed three experiments to improve grading accuracy. We found that giving students feedback about their grading bias increased subsequent accuracy. We introduce short, customizable feedback snippets that cover common issues with assignments, providing students more qualitative peer feedback. Finally, we introduce a data-driven approach that highlights high-variance items for improvement. We find that rubrics that use a parallel sentence structure, unambiguous wording, and well-specified dimensions have lower variance. After revising rubrics, median grading error decreased from 12.4p to 9.9p.