Overreacting to a black box

We often receive recommendations whose generation process is so complex that we cannot understand it. In such cases, we cannot perform accurate Bayesian updating. Moreover, it is well-documented that when such recommendations are unexpected for us, we often overreact to them. Based on the framework established by Ke, Wu, and Zhao (2024), we characterize an updating rule expressing such a reaction. In the resulting updating rule, if the distance between the recommendation and the decision maker’s prior belief is significant enough, she perceives it as unexpected and overreacts. This rule can be seen as a generalization of the contraction rule, proposed by Ke, Wu, and Zhao (2024).