DOI: 10.5061/dryad.79cnp5j7m
title: Scaling laws of political regime dynamics: Stability of democracies and autocracies in the 20th-century

description: In light of the current rise of authoritarian regimes and the anti-liberal
 tendencies in some established democracies, understanding the dynamic and
 statistical properties of political regimes is of critical importance.
 Despite their relevance, a comprehensive quantitative assessment of these
 dynamics on a historical scale remains largely unexplored, and the notion
 that democratization is an irreversible process has gone mostly
 unchallenged. This study provides a rigorous and quantitative analysis of
 political regimes worldwide by examining changes in freedoms of
 expression, association, and electoral quality throughout the 20th
 century. Utilizing the multidimensional V-Dem dataset, which covers over
 170 countries across more than a century, alongside tools from statistical
 physics, we demonstrate that historical political regime dynamics follow
 scaling laws, which are a hallmark of diffusion. We identify three
 distinct types of scaling laws in the data: super-diffusive behavior in
 destabilizing autocracies, random-walk dynamics in hybrid regimes, and
 sub-diffusive behavior in democracies and stable autocracies. Using these
 results, we also offer a novel perspective on the propensity of civil
 conflict.
description: # Scaling laws of political regime dynamics: Stability of democracies and
 autocracies in the 20th-century Dataset DOI:
 [10.5061/dryad.79cnp5j7m](10.5061/dryad.79cnp5j7m) ## Description of the
 data and file structure Data and Python scripts used to generate the
 analysis and figures used in the work under the title "Scaling laws
 of political regime dynamics – Stability of democracies and autocracies in
 the 20th-century". The source data was taken from the V-Dem project
 data set (v12) and the UCDP/PRIO Armed Conflict Dataset; and the code was
 developed by the authors. ### Files and variables #### File:
 vdem-anomalous-diff-results.py **Description:** Python code that generates
 all figures shown in the referenced work, taking the data
 from *data_vdem_dm.csv* and *output-msd-r-0p1-dm123-with-suffr-in-orig-t10.csv.* Warning: This code takes the V-Dem data and the armed conflict data from the file *data_vdem_dm.csv*, but the present version of this file does not include them. To run this code, this data must be previously accessed and added to this file. The group of V-Dem variables analysed can be derived from the “Varieties of Democracy” (V-Dem) project, version 12 (2022): [https://www.V-Dem.net](https://www.V-Dem.net). The data corresponding to armed conflict can be easily accessed via the UCDP Dataset Download Center ([https://ucdp.uu.se/downloads/](https://ucdp.uu.se/downloads/)). The variables considered in this work are the presence of ≤ 999 battle deaths/yr events and the presence of &gt; 999 battle deaths/yr events, both present in the UCDP/PRIO Armed Conflict Dataset. A detailed description of this data can be found in the following sources: * Davies, Shawn, Therese Pettersson & Magnus Öberg (2022). Organized violence 1989-2021 and drone warfare. Journal of Peace Research 59(4). * Gleditsch, Nils Petter, Peter Wallensteen, Mikael Eriksson, Margareta Sollenberg, and Håvard Strand (2002) Armed Conflict 1946-2001: A New Dataset. Journal of Peace Research 39(5). #### File: msd-dm.py **Description:** Python code that computes the Mean Squared Displacement (MSD) of the neighbourhood of each data point of the data set *data_vdem_dm.csv.* The input file is *data_vdem_dm.csv* and the output file is *output-msd-r-0p1-dm123-with-suffr-in-orig-t10.csv*.  Warning: This code takes the V-Dem data from the file *data_vdem_dm.csv*, but the present version of this file does not include it. To run this code, this data must be previously accessed and added to this file. The group of V-Dem variables analysed can be derived from the “Varieties of Democracy” (V-Dem) project, version 12 (2022): [https://www.V-Dem.net](https://www.V-Dem.net). #### File: output-msd-r-0p1-dm123-with-suffr-in-orig-t10.csv **Description:** Results from the python script *msd-dm.py* containing the MSD values of the neighbourhood of each data point of *data_vdem_dm.csv* in the space defined by the selected variables of the V-Dem project (version 12, [https://www.V-Dem.net](https://www.V-Dem.net)).  ##### Variables * index: Identifier of the data point being at the center of the neighbourhood in which the MSD is computed. It corresponds to the same index (row number) of the main data, where the data points are defined (*data_vdem*_*dm.csv*). * delta_1: MSD at time *t=1* year. * delta_2: MSD at time *t=2* years. * delta_3: MSD at time *t=3* years. * delta_4: MSD at time *t=4* years. * delta_5: MSD at time *t=5* years. * delta_6: MSD at time *t=6* years. * delta_7: MSD at time *t=7* years. * delta_8: MSD at time *t=8* years. * delta_9: MSD at time *t=9* years. * delta_10: MSD at time *t=10* years. #### File: data_vdem_dm.csv **Description:** This file contains the Diffusion Map manifold coordinates summarising the 25 V-Dem variables analysed. Each row contains the identification of the data point (country-year) and its manifold coordinates. ##### Variables * country_name: Official name of the country * country_text_id: International unique three-letter abbreviation of the country name * year: Year of assessment * dc1: First Diffusion Map coordinate  * dc2: Second Diffusion Map coordinate * dc3: Third Diffusion Map coordinate ## Code/software All code files provided are written in Python (v3.11.4). The main packages used are: pandas 2.3.0, numpy 1.26.4, statsmodels 0.14.0, scipy 1.15.2, scikit-learn 1.2.2, seaborn 0.12.2, and matplotlib 3.10.3. Additionally, pydiffmap 0.2.0.1 was used for the Diffusion Map creation, setting the parameters as detailed in "Scaling laws of political regime dynamics – Stability of democracies and autocracies in the 20th-century". The resulting manifold is in the data source file (*data_vdem_dm.csv*) under the variables dc1, dc2, and dc3 (Diffusion Map components 1, 2, and 3). ## Access information Other publicly accessible locations of the data: * 10.5281/zenodo.14851083 Data was derived from the following sources: * “Varieties of Democracy” (V-Dem) project, version 12 (2022): [https://www.V-Dem.net](https://www.V-Dem.net). * UCDP/PRIO Armed Conflict Dataset (2023): [https://ucdp.uu.se/downloads/](https://ucdp.uu.se/downloads/).