Grading Exams : 100, 99, ..., 1, or a, B, C?

We show that if students care primarily about their status (relative rank) in class, they are best motivated to work not by revealing their exact numerical exam scores (100, 99, ..., 1), but instead by clumping them in broad categories (A, B, C). If their abilities are disparate, the optimal grading scheme awards fewer A's than there are alpha-quality students, creating small elites. If their abilities are common knowledge, then it is better to grade them on an absolute scale (100 to 90 is an A, etc.) rather than on a curve (top 15% is an A, etc.). We develop criteria for optimal grading schemes in terms of the stochastic dominance between student performances