Paternalistic Information Design

How should a benevolent sender communicate private information to a receiver who updates beliefs in a systematically biased way? As an example, consider a hospital that has to communicate a test result to a patient prone to pessimistic inferences. I model this situation as a Bayesian sender observing an exogenous signal about the state of the world and choosing how to coarsen it before transmitting it to a receiver with updating biases. I show two main results: first, paternalistic information design can achieve first-best outcomes if and only if the sender can compress her information into categories that are both safe, meaning that they induce the receiver to take welfare-maximizing actions despite his biased updating, and lossless, meaning that they preserve the first-best value of the underlying information. Second, I show that the same decision problems for which information is most valuable under Bayesian updating are also the ones for which biased updating is hardest to mitigate through optimal information design. Together, these results characterize both the promise and the limits of paternalistic information design. Applications to medical reporting and AI-assisted lending show when coarsening information improves decisions and when it necessarily sacrifices first-best welfare.