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.

Hezbollah, the Iran-backed militia in Lebanon, fired three drones toward Israeli gas rigs this month in an area of the eastern Mediterranean claimed by Lebanon. Israeli officials said that the drones, which were quickly intercepted, did not carry arms of any kind and that they were launched only to show that Hezbollah is able to reach a point considered strategic and sensitive. The Israeli defense establishment has sophisticated air-defense mechanisms capable of intercepting rockets fired by enemies in Gaza, Lebanon and Syria. Israel also has a complex system of sensors able to detect tunnels that Palestinian and Lebanese militants sometimes dig under Israel's borders. But those defenses are relatively inefficient against the drone.