Reweights, retakes, and extra credit: A game-theoretic look at second chance grading

Students disappointed with their latest exam score frequently ask if it would be possible to de-emphasize that exam’s weight in determining their course grades, sometimes even asking to drop the exam altogether or retake the exam. Alternatively, students may ask to do an extra credit assignment to pull up their grades. Anticipating these requests, as well as strategic behavior by students, instructors should address them in their course syllabi.  Instructors typically have some choice about grading policies, and may opt for anything from a hard line system, with no second chance options and non-negotiable exam weights, to a lenient system in which a student may drop her lowest exam or increase the weight on her best exam.  Thus, each instructor must choose an optimal grading policy, though this choice may be fraught with numerous complications. For instance, an instructor might want to be sympathetic to student concerns and may doubt the accuracy of the recent exam score, but also wants to be fair to other students, honest with potential employers, and consistent with departmental norms. There are   downsides to writing new exams, comforting distraught students, developing a reputation as a pushover, or undermining one’s chances of tenure or renewal.  Each grading policy has costs and benefits; extra credit options might allow an instructor to gather useful information and encourage student effort, but may contribute to grade inflation and generate a negative externality for less lenient colleagues.  Also, each grading policy affects student behavior, both in terms of effort and evaluations, which may reward leniency and punish perceived unfairness.  E.g., if only underperformers can write an extra credit paper, then the system seems unfair –underperformers might be able to leapfrog their more satisfied peers – whereas if the paper is an option for everyone, then the top students might feel pressured to incur the cost of additional effort just to preserve their relative standing, even if their original exam score was satisfactory; in short, a policy intended to help the stragglers could harm the leaders.  To model this type of grading policy decision, we consider several related games between an instructor and multiple students. Considering the incentives of both parties, we predict how students will respond to each policy, and then compare policies from the instructor’s perspective.  Our general finding is that a wide variety of grading policies are observed because instructors have different preferences when it comes to offering second chances.