Phase transitions, marked by abrupt shifts in system features, are common in complex systems. While extensively studied in physical sciences, their empirical study in societal systems is underdeveloped. This research investigates whether collective civil unrest dynamics can be characterized as recurring phase shifts with measurable latent characteristics. Building on civil unrest modeling as a self-organized critical system, a macro-level statistical model is introduced and evaluated using a dataset encompassing 170 countries (1946-2017). The study aims to determine the plausibility of characterizing civil unrest as repeated phase shifts, explore if universal mechanisms govern certain aspects, assess global similarities/disparities in unrest intensity, and investigate the relationship between geographic location and long-term unrest intensity. Understanding the dynamics of civil unrest is crucial due to its profound impact on various facets of social life throughout history, influencing human rights, economic issues, independence movements, and religion. While there's a perceived increase in anti-government demonstrations, the intensity and frequency of civil unrest lack consistent patterns, characterized by periods of calm punctuated by bursts of high-intensity disorder. This bursty behavior is partially attributable to contagion and social influence mechanisms within communication and social networks. The study's approach for detecting regime changes remains viable even with incomplete understanding of all driving mechanisms, aligning with research emphasizing early-warning signals preceding shifts in complex systems. While detailed mechanistic models are challenging to construct, plausible models illuminating observed patterns enhance hypothesis credibility. Alternative mechanistic models, such as self-organized criticality, could also explain civil unrest's intermittent nature. Self-organized criticality models describe systems as governed by slow driving forces, gradually pushing the system into vulnerable states leading to energy dissipation in avalanches. A micro-dynamic model of civil unrest, an expanded forest-fire model, effectively replicates observed real-world dynamics, including transitions between calm and intense unrest. This model suggests a two-phase behavior of civil unrest, explained by time scale separation: unrest propagation is much faster than the rate at which regions become vulnerable to unrest. This micro-model provides a phenomenological perspective on civil unrest as a collective phenomenon undergoing self-organization and recurring phase transitions.

Existing research highlights the theoretical modeling of phase transitions in social systems but lacks empirical verification. While self-organization and phase transitions have been proposed in various domains, including human dynamics, financial markets, and opinion dynamics, empirical evidence remains scarce. Studies on protest recruitment bursts on Twitter, oscillating patterns of political instability, and Markov models for forecasting armed conflict phases highlight the potential for further investigation and the need for greater empirical validation. This study aims to fill this gap by applying statistical methods to detect and assess phase transitions in large-scale social systems, focusing on civil unrest. The approach differs from descriptive references to "waves," "spikes," and "bursts," instead identifying inherent and measurable latent phases. The analogy of "latent phases" to "climate" and "bursts" to "weather" is used to illustrate the concept. This rigorous approach allows for a deeper understanding of the underlying mechanisms behind civil disturbance.

The study examines civil unrest incidents reported in newspapers from 170 countries (1946-2017). A macro-level statistical model leveraging a hidden Markov model is employed to test the hypothesis of recurring latent phases underlying civil unrest. The model uses a "weighted conflict metric" time series, with unrest magnitude calculated as the logarithm of this metric. The macro-level phase model consists of an unobserved Markov chain governing latent phases and a phase-dependent process characterizing probability density functions generating observable civil unrest magnitudes. Phase-dependent normal distributions are used, allowing for flexibility in capturing both heavy-tailed and thin-tailed distributions. The model's parameters are estimated by maximizing the likelihood of observed data using the Baum-Welch algorithm. The Bayesian Information Criterion (BIC) determines the appropriate number of latent phases for each country. Goodness-of-fit Monte Carlo tests assess the model's suitability. The methodology includes generating synthetic data from the model and comparing its marginal distribution to the empirical distribution using Kolmogorov-Smirnov tests to assess goodness of fit at the individual country level. The study also uses several dimensionless quantities derived from the phase model to test universality (i.e. if there are universal mechanisms irrespective of country characteristics) and conducts geographic analyses using a scale quantifying a country’s long-term unrest per unit of time. Spatial autocorrelation using Moran's I statistic and Getis-Ord Local G statistic with random permutation tests are used to analyze regional patterns of civil unrest and determine significance of geographic clustering. The Viterbi algorithm determines the most probable sequence of latent phases from the observed data for visualization and illustrative purposes.

The macro-level phase model reveals distinct latent phases of civil unrest across countries. 81 countries showed two phases ("low" and "high"), five showed three, and 64 showed a single phase. For countries with two phases, the model accurately gauges expected magnitude and variability of unrest in each phase and the likelihood of transitions between them. The model successfully captures key summary statistics of the civil unrest data (mean, median, standard deviation, quartiles, min, max), suggesting its ability to represent overall data behavior. Goodness-of-fit tests support the hypothesis of recurring latent phases. Analysis of model features across continents reveals no statistically significant differences, suggesting potential universal distributions governing phase durations and unrest intensity/fluctuation ratios despite regional variations. Geographic analysis shows significant spatial correlation between a nation's unrest level and its neighbors, indicating geographically clustered civil unrest. A Kruskal-Wallis test reveals statistically significant variation in the magnitude scale of civil unrest between continents. The global hotspot analysis identifies clusters of countries with statistically significant high levels of civil unrest (primarily in North-Central Africa, the Middle East, Eastern Europe, South Asia, Southeast Asia, and Central Asia) and clusters with low levels (primarily in Southern and Western Europe, Northern Europe, East Asia, South America, Middle Africa, and Southern Africa). These spatial clustering observations align with historical accounts of civil unrest, exemplified by the Arab Spring, where observed geographic clustering of civil unrest in the figures, an emergent characteristic of the macro-level phase model, aligns with historical records of civil unrest on a global scale. This alignment reinforces the idea that recurring latent phases are a fundamental feature of civil unrest behavior. While these correlations do not necessarily imply causality, it may reflect both 'apparent' and 'true' contagion effects, necessitating further research.

The study's findings support the hypothesis of recurring latent phases in civil unrest, aligning with self-organized criticality models. The macro-level phase model provides a statistically plausible representation of civil unrest dynamics across diverse countries. The observed geographic clustering suggests the influence of both internal and external factors, highlighting potential contagion effects. The methodology can validate theoretical models and independently detect critical transitions, even without complete understanding of the underlying mechanisms. The model's parameters allow for forecasting civil unrest magnitude and phase prediction, offering potential for early warning systems. This approach complements early warning signal methodologies by exhibiting reduced sensitivity to data fluctuations. Policy implications include anticipating phase transitions to implement preventive measures, assessing vulnerability/resilience, and informing strategies for mitigating the impact of civil unrest. The model aids in identifying opportunities for desired phase transitions within social systems.

This study demonstrates that a macro-level phase model effectively captures the dynamics of civil unrest across countries and time, suggesting the presence of recurring latent phases. Geographic analysis reveals significant spatial clustering of civil unrest events. The findings support the use of the model for forecasting and early warning purposes, offering valuable insights for policymakers and researchers. Future research should focus on investigating contagion processes and exploring the application of this methodology to other collective human phenomena.

The study relies on newspaper reports for civil unrest data, which may introduce geographic bias and underreporting of events. The model is a phenomenological representation and doesn't provide a precise mechanistic explanation of all factors driving civil unrest. While spatial clustering is observed, the analysis cannot definitively distinguish between 'apparent' and 'true' contagion.