Collective intelligence refers to the ability of groups to outperform individual decision-makers. At present, relatively little is known about the mechanisms promoting collective intelligence in natural systems. We here test a novel mechanism generating collective intelligence: self-organization according to information quality. We tested this mechanism by performing simulated predator detection experiments using human groups. By continuously tracking the personal information of all members prior to collective decisions, we found that individuals adjusted their response time during collective decisions to the accuracy of their personal information. When individuals possessed accurate personal information, they decided quickly during collective decisions providing accurate information to the other group members. By contrast, when individuals had inaccurate personal information, they waited longer, allowing them to use social information before making a decision. Individuals deciding late during collective decisions had an increased probability of changing their decision leading to increased collective accuracy. Our results thus show that groups can self-organize according to the information accuracy of their members, thereby promoting collective intelligence. Interestingly, we find that individuals flexibly acted both as leader and as follower depending on the quality of their personal information at any particular point in time.