Learning from Black Boxes
Shaowei Ke, University of Michigan
Monday, May 2, 2022
We study a decision maker's learning behavior when she receives recommendations from black boxes, i.e., the decision maker does not understand how the recommendations are generated. We introduce three types of axioms to be imposed on the decision maker's learning rule, (weak and strong) monotonicity, (weak and strong) regularity, and partial obedience. We show that strong monotonicity and weak regularity characterize the contraction rule, which has two parameters that map each recommendation to a recommended belief and to the trustworthiness of the recommendation. The decision maker's posterior is formed by mixing her prior with the recommended belief weighted by the trustworthiness measure. We show that under weak monotonicity, partial obedience, and strong regularity, the learning rule must feature a form of conservatism. However, no contraction rules are conservative; i.e., there does not exist any learning rule that satisfies strong monotonicity, partial obedience, and strong regularity simultaneously.