Leadership is widespread across the animal kingdom. In self-organizing groups, such as fish schools, theoretical models predict that effective leaders need to balance goal-oriented motion, such as toward a known resource, with their tendency to be social. Increasing goal orientation is predicted to increase decision speed and accuracy, but it is also predicted to increase the risk of the group splitting. To test these key predictions, we trained fish (golden shiners, Notemigonus crysoleucas) to associate a spatial target with a food reward ("informed" individuals) before testing each singly with a group of eight untrained fish who were uninformed ("naive") about the target. Informed fish that exhibited faster and straighter paths (indicative of greater goal orientation) were more likely to reach their preferred target and did so more quickly. However, such behavior was associated with a tendency to leave untrained fish behind and, therefore, with failure to transmit their preference to others. Either all or none of the untrained fish stayed with the trained fish in the majority of trials. Using a simple model of self-organized coordination and leadership in groups, we recreate these features of leadership observed experimentally, including the apparent consensus behavior among naive individuals. Effective leadership thus requires informed individuals to appropriately balance goal-oriented and socially oriented behavior.