Psychologists typically measure beliefs and preferences using self-reports, whereas economists are much more likely to infer them from behavior. Prediction markets appear to be a victory for the economic approach, having yielded more accurate probability estimates than opinion polls or experts for a wide variety of events, all without ever asking for self-reported beliefs. We conduct the most direct comparison to date of prediction markets to simple self-reports using a within-subject design. Our participants traded on the likelihood of geopolitical events. Each time they placed a trade, they first had to report their belief that the event would occur on a 0–100 scale. When previously validated aggregation algorithms were applied to self-reported beliefs, they were at least as accurate as prediction-market prices in predicting a wide range of geopolitical events. Furthermore, the combination of approaches was significantly more accurate than prediction-market prices alone, indicating that self-reports contained information that the market did not efficiently aggregate. Combining measurement techniques across behavioral and social sciences may have greater benefits than previously thought.