  We introduce and study the problem of detecting whether an agent is updating
their prior beliefs given new evidence in an optimal way that is Bayesian, or
whether they are biased towards their own prior. In our model, biased agents
form posterior beliefs that are a convex combination of their prior and the
Bayesian posterior, where the more biased an agent is, the closer their
posterior is to the prior. Since we often cannot observe the agent's beliefs
directly, we take an approach inspired by information design. Specifically, we
measure an agent's bias by designing a signaling scheme and observing the
actions they take in response to different signals, assuming that they are
maximizing their own expected utility; our goal is to detect bias with a
minimum number of signals. Our main results include a characterization of
scenarios where a single signal suffices and a computationally efficient
algorithm to compute optimal signaling schemes.
