Population density and size facilitate interactive capacity and the rise of the state.

Radiocarbon summed probability distribution (SPD) methods promise to illuminate the role of demography in shaping prehistoric social processes, but theories linking population indices to social organization are still uncommon. Here, we develop Power Theory, a formal model of political centralization that casts population density and size as key variables modulating the interactive capacity of political agents to construct power over others. To evaluate this argument, we generated an SPD from 755 radiocarbon dates for 10 000-1000 BP from Central, North Central and North Coast Peru, a period when Peruvian political form developed from 'quasi-egalitarianism' to state levels of political centralization. These data are congruent with theoretical expectations of the model but also point to an artefactual distortion previously unremarked in SPD research. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.