Optimized collusion prevention for online exams during social distancing

摘要

Assume that collusion happens between two students and one can get answers from the other on questions that the other has already answered or is working on (see “Methods”). a The circulation-based scheme is illustrated with a simple example, in which six students take an exam consisting of six questions (M1 = M2 = 6) provided to each student one by one, and each question must be finished within the allocated time slot shown as the vertical box. If there is no information of students' competences, this scheme helps reduce potential bidirectional cheating among students to ~50% of question; b the collusion chance can be made even less if cheating students are fed with more new questions (M1 = 4, M2 = 6); c if prior information on students' competences is available, the naive assignment in b still yields significant collusion gains; but d, using our grouping-based anti-collusion scheme, the maximum and average collusion gains can be sharply reduced to ~10% and ~3%, respectively. The scheme first divides the competence range into M2 − M1 + 1 intervals, then groups the students into these intervals properly, finally assigns these groups of students with the corresponding number of consecutive cyclic sequences, respectively. The maximum collusion gain with this scheme is bounded by our Theorem 1.