It is suggested that the size of a population to some extent defines the limits of its social complexity. State level societies tend to have relatively large populations, and egalitarian communities tend to be relatively small. Since the 1960s, anthropologists have tried to describe and explain this relationship between population size and social complexity, suggesting a causal link between large populations and social differentiation, based on studies of game theory and human cognitive capacity. Once a population rises above a certain level, change in social organisation is deemed inevitable. Approximate figures for these ‘population thresholds’ have been proposed, but their accuracy and applicability to archaeological populations and communities remain uncertain. This paper explores the hypothetical population threshold at the point when societies begin to show the first signs of ranking in the context of the Early Bronze Age Aegean, comparing the estimated population sizes of particular sites with the evidence they show for ranking and social hierarchy. While larger communities tend to show more evidence for social differentiation, it is recognised that population size is not the sole factor in determining its development.