{"pk":38285,"title":"The Growth and Decline of the Western Roman Empire: Quantifying the Dynamics of Army Size, Territory, and Coinage","subtitle":null,"abstract":"We model the Western Roman Empire from 500 BCE to 500 CE, aiming to understand the interdependent dynamics of army size, conquered territory and the production and debasement of coins within the empire. The relationships are represented through feedback relationships and modelled mathematically via a dynamical system, specified as a set of ordinary differential equations. We analyze the stability of a subsystem and determine that it is neutrally stable. Based on this, we find that to prevent decline, the optimal policy was to stop debasement and reduce the army size and territory during the rule of Marcus Aurelius. Given the nature of the stability of the system and the kind of policies necessary to prevent decline, we argue that a high degree of centralized control was necessary, in line with basic tenets of structural-demographic theory.\n \nThis article was updated on 01/09/2020 to correct an error in equation (3.5). Page numbers were updated on 01/05/2021.","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Roman Empire"},{"word":"Dynamical System"},{"word":"Differential Equations"},{"word":"Debasement"},{"word":"societal collapse"}],"section":"Article","is_remote":true,"remote_url":"https://escholarship.org/uc/item/2cz4q2jq","frozenauthors":[{"first_name":"Sabin","middle_name":"","last_name":"Roman","name_suffix":"","institution":"Centre for the Study of Existential Risk, University of Cambridge\nRomanian Institute of Science and Technology, Romania","department":"None"},{"first_name":"Erika","middle_name":"","last_name":"Palmer","name_suffix":"","institution":"Ruralis - Institute for Rural and Regional Research","department":"None"}],"date_submitted":"2019-05-10T08:59:39-04:00","date_accepted":"2019-05-10T08:59:39-04:00","date_published":"2019-12-30T03:00:00-05:00","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/cliodynamics/article/38285/galley/28810/download/"}]}