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Grading exams: 100,99,98,\(\dots \) or \(A,B,C\)? (English) Zbl 1229.91091
Summary: We introduce grading into games of status. Each player chooses effort, producing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incentives to work are changed.
We apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100,99,\(\dots ,1\)), but instead by clumping them into coarse categories \((A,B,C)\).
When student abilities are disparate, the optimal absolute grading scheme is always coarse. Furthermore, it awards fewer \(A\)’s than there are alpha-quality students, creating small elites. When students are homogeneous, we characterize optimal absolute grading schemes in terms of the stochastic dominance between student performances (when they shirk or work) on subintervals of scores, showing again why coarse grading may be advantageous.In both cases, we prove that absolute grading is better than grading on a curve, provided student scores are independent.

MSC:
91A80 Applications of game theory
91A60 Probabilistic games; gambling
91A10 Noncooperative games
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