Overinference from Weak Signals and Underinference from Strong Signals

We study how overreaction and underreaction to signals depend on their informativeness. While a large literature has studied belief updating in response to highly informative signals, people in important real-world settings are often faced with a steady stream of weak signals. We use a tightly controlled experiment and new empirical evidence from betting and financial markets to demonstrate that updating behavior differs meaningfully by signal strength: across domains, our consistent and robust finding is overreaction to weak signals and underreaction to strong signals. Both sets of results align well with a simple theory of cognitive imprecision about signal informativeness. Our framework and findings can help harmonize apparently contradictory results from the experimental and empirical literatures.