Recent studies have demonstrated that human societies are hierarchically structured, with a consistent scaling ratio of between three and four across successive layers of the social network. Here we used Horton-Strahler scaling to show that similar relationships hold for four mammalian taxa living in multi-level social systems. For elephant, gelada and hamadryas baboon, successive layers of social organisation have a scaling ratio of almost exactly three, indicating that such branching ratios may be a consistent feature of all hierarchically structured societies. Interestingly, the scaling ratio for orca was 3.8, which might mean that aquatic environments place different constraints on the organisation of social hierarchies. However, circumstantial evidence from a range of other species suggests that scaling ratios close to three may apply widely, even in species where hierarchical social structures have not traditionally been identified. These results identify the origin of the hierarchical, fractal-like organization of mammalian social systems as a fundamental question.