Supplementary material from "From disorganized equality to efficient hierarchy: how group size drives the evolution of hierarchy in human societies"

A manifest trend is that larger and more productive human groups shift from distributed to centralized decision-making. Voluntary theories propose that human groups shift to hierarchy to limit scalar stress, i.e. the increase in cost of organization as a group grows. Yet, this hypothesis lacks a mechanistic model to investigate the organizational advantage of hierarchy and its role on its evolution. To fill this gap, we describe social organization by the distribution of individuals’ capacity to influence others. We then integrate this formalization into models of social dynamics and evolutionary dynamics. First, our results demonstrate that hierarchy strongly reduces scalar stress, and that this benefit can emerge solely because leaders and followers differ in their capacity to influence others. Second, the model demonstrates that this benefit can be sufficient to drive the evolution of leader and follower behaviours and ultimately, the transition from small egalitarian to large hierarchical groups.