Peer pressure can induce sudden, unexpected changes in the behavior of a group. With agent-based simulations, we study the impact of one individual on the behavior of a social network of people. We find that an individual with the largest benefit dominates the group behavior. If that individual happens to have a leadership role, the impact is particularly strong. The model suggests that even if the average benefit for the group changes slowly, the average participation changes suddenly but with a delay. The delay is shorter if the network is subject to large, unpredictable outside influences. Further, we find that incentives that target leaders are more effective than unspecific incentives. We discuss applications of the model to the dynamics of membership in an agricultural youth organization.