Optimal adaptive testing: Informativeness and incentives

Abstract

We introduce a learning framework in which a principal seeks to determine the ability of a strategic agent. The principal assigns a test consisting of a finite sequence of tasks. The test is adaptive: each task that is assigned can depend on the agent's past performance. The probability of success on a task is jointly determined by the agent's privately known ability and an unobserved effort level that he chooses to maximize the probability of passing the test. We identify a simple monotonicity condition under which the principal always employs the most (statistically) informa- tive task in the optimal adaptive test. Conversely, whenever the condition is violated, we show that there are cases in which the principal strictly prefers to use less informative tasks. We discuss the implication of our results for task assignment in organizations with the aim of determining suitable candidates for promotions.