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The social brain hypothesis predicts that species with relatively larger neocortices should exhibit more complex social strategies than those with smaller neocortices. We test this prediction using data on the correlation between male rank and mating success for polygamous primates. This correlation is negatively related to neocortex size, as would be predicted if males of species with large neocortices are more effective at exploiting social opportunities to undermine the dominant male's power-based monopolisation of peri-ovulatory females than are those with smaller neocortices. This effect is shown to be independent of the influence of male cohort size.