Hamilton, Marcus J.; Robert S. Walker; Briggs Buchanan and David S. Sandeford

Human societies exhibit a diversity of social organizations that vary widely in size, structure, and complexity. Today, human sociopolitical complexity ranges from stateless small-scale societies of a few hundred individuals to complex states of millions, most of this diversity evolving only over the last few hundred years. Understanding how sociopolitical complexity evolved over time and space has always been a central focus of the social sciences. Yet despite this long-term interest, a quantitative understanding of how sociopolitical complexity varies across cultures is not well developed. Here we use scaling analysis to examine the statistical structure of a global sample of over a thousand human societies across multiple levels of sociopolitical complexity. First, we show that levels of sociopolitical complexity are self-similar as adjacent levels of jurisdictional hierarchy see a four-fold increase in population size, a two-fold increase in geographic range, and therefore a doubling of population density. Second, we show how this self-similarity leads to the scaling of population size and geographic range. As societies increase in complexity population density is reconfigured in space and quantified by scaling parameters. However, there is considerable overlap in population metrics across all scales suggesting that while more complex societies tend to have larger and denser populations, larger and denser populations are not necessarily more complex.