Mathematical model of group work

Abstract

Peer assessment, or peer evaluation, is an essential tool in group projects within educational settings, particularly in large-scale classrooms where direct instructor oversight is limited. It plays a key role in addressing the free rider problem, where some students contribute minimally yet receive equal credit as their group members. In this paper, we propose a mathematically rigorous peer assessment model grounded in game theory to mitigate issues of strategic manipulation, collusion, and insincere reporting, which commonly undermine the validity and reliability of existing mechanisms. Our model represents peer evaluations as a matrix and uses row medians to determine the perceived contribution of each student. To promote truthful reporting, we introduced a consistency score that combines the Spearman correlation coefficient and the Euclidean distance, capturing both rank order and magnitude-based discrepancies in evaluations. This dual approach incentivises honest reporting by aligning students’ best responses with truth-telling. We briefly demonstrate that the model satisfies essential educational criteria of validity, reliability, and practicality, providing a foundation for fairer and more robust peer evaluation systems in collaborative learning environments.