Scores and Rewards: Evaluation Design for Learning Processes

Learners are evaluated repeatedly throughout the learning process. Each period, a noisy signal of performance arrives, and the principal must decide how to combine past and present signals into a score, and how to reward it. This paper studies the optimal design of such scores. An agent exerts costly effort that shifts a persistent performance signal. The principal cares about two things: the accuracy of the score as an estimate of true performance, and the incentives the score creates. In this paper, we characterize the optimal scoring rule over past signals in closed form using spectral methods.  We find that the optimal incentive rewards the current period heavily and ‘claws back’ that reward in later periods. Accuracy and incentives call for opposite treatments of history: one adds history to improve accuracy, because history contains information, but subtracts history to sharpen incentives, because past performance has already been rewarded. The two objectives therefore pull the weights in opposite directions. Our results hold over a wide range of learning processes, and they offer guidance for the design of learning and evaluation systems.