In most group-living animals, a dominance hierarchy reduces the costs of competition for limited resources. Dominance ranks may reflect prior attributes, such as body size, related to fighting ability or reflect the history of self-reinforcing effects of winning and losing a conflict (the winner-loser effect), or both. As to prior attributes, in sexually dimorphic species, where males are larger than females, males are assumed to be dominant over females. As to the winner-loser effect, the computational model DomWorld has shown that despite the female’s lower initial fighting ability, females achieve some degree of dominance of females over males. In the model, this degree of female dominance increases with the proportion of males in a group. This increase was supposed to emerge from the higher fraction of fights of males among themselves. These correlations were confirmed in despotic macaques, vervet monkeys, and in humans. Here, we first investigate this hypothesis in DomWorld and next in long-term data of 9,300 observation hours on six wild groups of robust capuchin monkeys (Sapajus libidinosus; S. nigritus, and S. xanthosternos) in three Brazilian sites. We test whether both the proportion of males and degree of female dominance over males are indeed associated with a higher relative frequency of aggression among males and a higher relative frequency of aggression of females to males. We confirm these correlations in DomWorld. Next, we confirm in empirical data of capuchin monkeys that with the proportion of males in the group there is indeed an increase in female dominance over males, and in the relative frequency of both male-male aggression and aggression of females to males and that the female dominance index is significantly positively associated with male male aggression. Our results reveal that adult sex ratio influences the power relation between the sexes beyond predictions from socioecological models.