Once considered provocative1, the notion that the wisdom of the crowd is superior to any individual has become itself a piece of crowd wisdom, leading to speculation that online voting may soon put credentialed experts out of business2,3. Recent applications include political and economic forecasting4,5, evaluating nuclear safety6, public policy7, the quality of chemical probes8, and possible responses to a restless volcano9. Algorithms for extracting wisdom from the crowd are typically based on a democratic voting procedure. They are simple to apply and preserve the independence of personal judgment10. However, democratic methods have serious limitations. They are biased for shallow, lowest common denominator information, at the expense of novel or specialized knowledge that is not widely shared11,12. Adjustments based on measuring confidence do not solve this problem reliably13. Here we propose the following alternative to a democratic vote: select the answer that is more popular than people predict. We show that this principle yields the best answer under reasonable assumptions about voter behaviour, while the standard ‘most popular’ or ‘most confident’ principles fail under exactly those same assumptions. Like traditional voting, the principle accepts unique problems, such as panel decisions about scientific or artistic merit, and legal or historical disputes. The potential application domain is thus broader than that covered by machine learning and psychometric methods, which require data across multiple questions14,15,16,17,18,19,20.