Teamwork makes the dream work: mathematical model of group work

• Main Author: Lee, Megan Zheng Chi
• Other Authors: Fedor Duzhin
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Mathematical Sciences; Mathematical model; Group work; Peer evaluation
• Online Access: https://hdl.handle.net/10356/175629
• Institution: Nanyang Technological University

Group work is widely employed in educational settings across different fields because of its benefits in developing soft and hard skills. As unequal contributions often happen in collaborative settings, peer evaluations offer insights into an individual’s contribution to the task to course instructors to assign individual scores. As students are naturally interested in maximising their scores and may game the system, the peer evaluation process may be studied from a mathematical and game-theoretic lens. Eight grading mechanisms are introduced. A common mechanism used in practice is Pie-to-others, which returns the average of scores received by a student from their team members. Using a large dataset of peer evaluations from several courses, Pie-to-others was found to be about 1% unreliable. A worst-case scenario of discrepancies in scores were also evaluated and the error was found to be largest when the contribution is minimal. Other theoretical properties such as monotonic behaviour, collective truth-telling as a weak Nash equilibrium, strong reliability and tolerance level for zero reporting were examined. Finally, the mechanisms were improved by including a consistency score to alter collective truth-telling to become a strict Nash equilibrium. From a psychometric perspective, Median Pie-to-all and Ration-the-mean-pie are mechanisms we recommend to implement in practice. These peer evaluation mechanisms are easy to implement for educators while simultaneously retaining elegant theoretical properties. Some of the results here will be presented at The Paris Conference on Education (PCE2024).