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During the Holocene, the scale and complexity of human societies increased markedly. Generations of scholars have proposed different theories explaining this expansion, which range from broadly functionalist explanations, focusing on the provision of public goods, to conflict theories, emphasizing the role of class struggle or warfare. To quantitatively test these theories, we develop a general dynamical model based on the theoretical framework of cultural macroevolution. Using this model and Seshat: Global History Databank, we test 17 potential predictor variables proxying mechanisms suggested by major theories of sociopolitical complexity (and >100,000 combinations of these predictors). The best-supported model indicates a strong causal role played by a combination of increasing agricultural productivity and invention/adoption of military technologies (most notably, iron weapons and cavalry in the first millennium BCE).