Social dominance hierarchies are widespread, but little is known about the mechanisms that produce non-linear structures. In addition to despotic hierarchies, where a single individual dominates, shared hierarchies exist where multiple individuals occupy a single rank. Our model shows that all three hierarchy structures–linear, despotic, and shared–can emerge from different combinations of simple interactions present in social insects. Our model shows that a linear hierarchy emerges when a typical winner-loser interaction (dominance biting) is present. A despotic hierarchy emerges when a policing interaction is added that results in the complete loss of dominance status for an attacked individual (physical policing). Finally, a shared hierarchy emerges with the addition of a “winner-winner” interaction that results in a positive outcome for both interactors (antennal dueling).