Self-organizing-system approaches have shed significant light on the mechanisms underlying synchronized movements by large groups of animals, such as shoals of fish, flocks of birds, or herds of ungulates. However, these approaches rarely consider conflicts of interest between group members, although there is reason to suppose that such conflicts are commonplace. Here, we demonstrate that, where conflicts exist, individual members of self-organizing groups can, in principle, increase their influence on group movement destination by strategically changing simple behavioral parameters (namely, movement speed, assertiveness, and social attraction range). However, they do so at the expense of an increased risk of group fragmentation and a decrease in movement efficiency. We argue that the resulting trade-offs faced by each group member render it likely that group movements are led by those members for which reaching a particular destination is most crucial or group cohesion is least important. We term this phenomenon leading according to "need" or "social indifference," respectively. Both kinds of leading can occur in the absence of knowledge of or communication about the needs of other group members and without the assumption of altruistic cooperation. We discuss our findings in the light of observations on fish and other vertebrates.