Conflicts of interest about where to go and what to do are a primary challenge of group living. However, it remains unclear how consensus is achieved in stable groups with stratified social relationships. Tracking wild baboons with a high-resolution global positioning system and analyzing their movements relative to one another reveals that a process of shared decision-making governs baboon movement. Rather than preferentially following dominant individuals, baboons are more likely to follow when multiple initiators agree. When conflicts arise over the direction of movement, baboons choose one direction over the other when the angle between them is large, but they compromise if it is not. These results are consistent with models of collective motion, suggesting that democratic collective action emerging from simple rules is widespread, even in complex, socially stratified societies.