Abstract In many species, cultures, and contexts, social dominance reflects the ability to exert influence over others, and the question of what makes an effective leader is pertinent to a range of disciplines and contexts. While dominant individuals are often assumed to be most influential, the behavioral traits that make them dominant may also make them socially aversive and thereby reduce their influence. Here we examine the influence of dominant and subordinate males on group behavior in different social contexts using the cichlid fish Astatotilapia burtoni . We find that phenotypically dominant males display behavioral traits that typify leadership across taxonomic systems – aggressive, social centrality, and movement leadership, while subordinate males are passive, socially peripheral, and have little influence over movement. However, in a more complex group-consensus task involving visual cue associations, subordinate males become the most effective agents of social change. We find that dominant males are spatially distant and have lower signal-to-noise ratios of informative behavior in the association task, potentially interfering with their ability to generate group-consensus. In contrast, subordinate males are physically close to other group members, have high signal-to-noise behaviors in the association task, and visual connectivity to other group members equal to that of dominant males. The attributes that define effective social influence are therefore highly context-specific, with socially and phenotypically dominant males being influential in routine but not complex social scenarios. These results demonstrate that behavioral traits that are typical of socially dominant individuals may actually reduce their social influence in other contexts. Significance Statement The attributes that allow individuals to attain positions of social power and dominance are common across many vertebrate social systems – aggression, intimidation, coercion. Yet these traits are socially aversive, and can make dominant individuals poor agents of social change. In a vertebrate system (social cichlid fish) we show that dominant males are aggressive, socially central, and lead group movement. Yet dominant males are poor effectors of consensus in an more sophisticated association task compared with passive, socially-peripheral subordinate males. The most effective agents of social influence possess behavioral traits opposite of those typically found in position of social dominance, suggesting the behavioral processes that generate social dominance may simultaneously place the most ineffective leaders in positions of power.