Animals that live together in groups often face difficult choices, such as which food resource to exploit, or which direction to flee in response to a predator. When there are costs associated with deadlock or group fragmentation, it is essential that the group achieves a consensus decision. Here, we study consensus formation in emigrating ant colonies faced with a binary choice between two identical nest-sites. By individually tagging each ant with a unique radio-frequency identification microchip, and then recording all ant-to-ant 'tandem runs'-stereotyped physical interactions that communicate information about potential nest-sites-we assembled the networks that trace the spread of consensus throughout the colony. Through repeated emigrations, we show that both the order in which these networks are assembled and the position of each individual within them are consistent from emigration to emigration. We demonstrate that the formation of the consensus is delegated to an influential but exclusive minority of highly active individuals-an 'oligarchy'-which is further divided into two subgroups, each specialized upon a different tandem running role. Finally, we show that communication primarily occurs between subgroups not within them, and further, that such between-group communication is more efficient than within-group communication.