Coordination and consensus in collective behavior have attracted a lot of research interest. Although previous studies have investigated the role of compromisers in group consensus, they provide little insight into why compromisers would allow such social arrangements to persist. In this study, the potential relationship between group movements and conflict management in Tibetan macaques in Anhui province, China, was investigated using hierarchical cluster analyses. Some members with higher social centrality or social rank often formed a front-runner cluster during group movements. They had higher leadership success than individuals outside the front-runner cluster. Other members with lower social centrality or social rank often followed the group movements initiated by the front-runner cluster, and thus formed the compromiser cluster. Compromisers\' proximity relations with front-runners increased with their following scores to front-runners. Compromisers had fewer events of being attacked when they followed group movements initiated by the front-runners. The compromising process made compromisers lose the choice of direction preference, but it could increase their individual safeties. This trade-off suggests that compromisers play a role of decision-maker in coordination and consensus scenarios among social animals.