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’.

放射性碳总和概率分布 (SPD) 方法有望阐明人口统计学在塑造史前社会过程中的作用，但将人口指数与社会组织联系起来的理论仍然不常见。在这里，我们发展了权力理论，这是一种政治集权的正式模型，它将人口密度和规模作为关键变量，调节政治代理人的互动能力，以构建对他人的权力。为了评估这一论点，我们从秘鲁中部、中北部和北部海岸的 10 000-1000 BP 的 755 个放射性碳日期生成了 SPD，该时期秘鲁的政治形式从“准平均主义”发展到国家层面的政治集权。这些数据与模型的理论预期一致，但也指出了以前在 SPD 研究中未发现的人为失真。

本文是主题问题“史前人口学的跨学科方法”的一部分。