Extremist ideology as a complex contagion: the spread of far-right radicalization in the United States between 2005 and 2017

The far-right movement in the United States—including white supremacists, neo-Nazis, and sovereign citizens—is the oldest and most deadly form of domestic extremism. It has been responsible for a large majority of extremist murders in recent years, with public concern heightened by increased violence and amplified rhetoric on social media. Prior work suggests radicalization is not primarily driven by psychopathology, but is a process involving destabilization by environmental (endemic) factors, exposure to extremist ideology, and reinforcement by communities. Even so-called lone actors often engage with online extremist communities. The study posits that radicalization may spread as a social contagion, specifically a complex contagion requiring multiple exposures for adoption, a pattern seen in broader political movements. Related phenomena—extremist propaganda diffusion, hate crimes, intergroup conflict, and terrorism—display contagion-like dynamics. Endemic factors such as poverty and other socio-demographics may enhance or constrain the spread across geographic space, yet few studies have examined how such endemic factors interact with contagion processes. The research aims to test whether patterns of far-right radicalization in the U.S. are consistent with a contagion process and to assess key endemic factors, after controlling for population density: poverty, unemployment, income inequality, education, non-white population size, violent crime, gun ownership, hate groups per capita, and Republican voting. It also examines whether individual-level variables (social media use, group membership) enhance spread over space and time, given evidence that social media both facilitates recruitment and reflects spatial clustering of social ties and diffusion. The study employs a two-component spatio-temporal intensity (twinstim) model that treats events as self-exciting point processes, separating endemic and epidemic components to assess both spatio-temporal covariates and contagion effects. Radicalization events are taken from the PIRUS database, which includes U.S.-radicalized individuals tied to ideologically motivated crimes or violent extremist organizations and provides individual-level social variables relevant to diffusion.

Prior literature indicates that extremist processes can exhibit contagion dynamics: propaganda diffusion on social networks, spatial clustering of hate crimes, intergroup conflict propagation, and terrorism diffusion have been documented. Complex contagions requiring multiple exposures have been observed in political mobilization more broadly. Environmental correlates of radicalization, extremism, and mass shootings identified in earlier work include poverty, unemployment, income inequality, education, racial composition, violent crime, gun ownership, hate group prevalence, and political voting patterns. Social media is shown to serve as a recruitment tool and space for community reinforcement, often augmenting physical organizing. Despite relaxed geographic constraints online, social media networks remain spatially clustered, implying that online diffusion of extremist ideology may retain geographic bias. The study builds on this literature by jointly modeling contagion and endemic factors in space and time using individual-level data from PIRUS.

Design: Observational spatio-temporal point process analysis using a two-component spatio-temporal intensity (twinstim) model in R (surveillance package). Data sources and sample: - Individual-level data: PIRUS (START). Inclusion: far-right ideology; exposure during/after 2005 (earliest social media data); geocoded to city-level or finer (n=416; 6.0% female, 94.0% male). - Variables per individual: date and location of exposure; plot success (34.9%); anticipated fatalities (0: 69.5%, 1–20: 26.0%, >20: 2.6%, >100: 1.9%); group membership (formal/informal) (58.4%); social media role in radicalization (31.2%). Unknown/missing values coded as 0 (plot success: 0.5%, fatalities: 13.5%, group membership: 0%, social media: 54.8%). Robustness check with multiple imputation via chained equations and random forest confirmed consistency. - Geocoding: nearest city/town using ggmap. Assumption: exposure location approximates radicalization location based on domestic terrorists’ local activity patterns. Endemic covariates: - County-level: log population density (offset), poverty rate, Gini index, percent non-white, percent with ≥ high-school diploma, unemployment rate; county-level income/race/education/unemployment from 2010 used for 2005–2009 due to availability. - County-level political: presidential election Republican voting share; non-election years assigned most recent election’s values. - State-level: gun ownership proxy, hate groups per capita, violent crime rate. Gun ownership proxy (state-level): (0.62 × FS/S) + (0.88 × HL) − 0.0448, where FS/S is the firearm-suicide proportion (CDC) and HL is hunting licenses per capita (USFWS), following Seigel et al. (R^2=0.95 with observed ownership). Missing suicide rates imputed with state means. Geographic data: US Census (tigris package). Model specification: - Twinstim model with endemic and epidemic components; tied locations/dates jittered randomly up to half the minimum spatial (1.52 km) and temporal (0.5 days) distances to form a continuous point process. - Interaction kernels: Step functions for space and time based on pair correlation indicating clustering up to 400 km. Spatial steps: four bins of 0–100, 100–200, 200–300, 300–400 km (max radius 400 km). Temporal steps: four bins of 0–6, 6–12, 12–18, 18–24 months (max 2 years). - Alternative kernels (power-law, Gaussian, Student for space; exponential for time) were tested but yielded unrealistically steep decays, sensitive to tie-breaking, so step functions were retained. - Endemic component: log(population density) as offset; centered linear time trend; dynamic annual predictors: poverty, Gini, percent non-white, percent ≥ high-school diploma, unemployment, Republican voting, violent crime per 1,000 residents, hate groups per million; state/county as above. - Epidemic predictors (event-level): plot success, anticipated fatalities, group membership, social media role. Model selection and inference: - Exhaustive set of models with all predictor combinations; ranked by AIC. Best-fitting (lowest AIC, ΔAIC<2) model retained. - Effects reported as rate ratios (exp of coefficients) with Wald CIs and p-values. Contagion significance testing: - Monte Carlo permutation test: Base model with endemic predictors only vs. 1,000 time-shuffled permutations; estimated reproduction number R0 for each; p-value from observed R0 vs. null distribution of converged permutations. - Additional tests: Likelihood ratio test (epidemic vs endemic-only), and Knox test (space-time clustering) using 100 km and 6-month thresholds. Model validation: - Simulations using Ogata’s modified thinning algorithm: 1,000 simulations of the last six months (Jun 2017–Jan 2018) from cumulative intensity; compared cumulative counts and spatial kernels to observed.

- Evidence of contagion: Observed reproduction number R0 = 0.31, significantly greater than permutation null (Nconv=739, p<0.01). Likelihood ratio test and Knox test also significant (p<0.0001), indicating non-random spatio-temporal clustering attributable to an epidemic component. - Time trend: Endemic rate declines 4.6% per year (RR=0.946; 95% CI: 0.91–0.98; p=0.0015), implying relatively stronger epidemic contribution over time. Baseline endemic increase around 2008–2012 (likely financial crisis) and epidemic spike around 2016 (presidential election) observed in intensity plots. Endemic predictors (best-fitting model): - Poverty rate: Positive association (RR=1.052; 95% CI: 1.02–1.09; p=0.0025). - Hate groups per capita: Positive association (RR=1.191; 95% CI: 1.12–1.27; p<0.0001). - Republican voting share: Negative association (RR=0.969; 95% CI: 0.96–0.98; p<0.0001). Competitiveness (absolute party vote difference) not significant when substituted. - Percent non-white: Negative association (RR=0.989; 95% CI: 0.98–1.00; p=0.038). - Unemployment rate: Negative association (RR=0.871; 95% CI: 0.82–0.93; p<0.0001). - Education level: Not statistically significant (RR=0.980; 95% CI: 0.96–1.00; p=0.075). - Violent crime rate: Not significant (RR=0.930; 95% CI: 0.84–1.03; p=0.17). - Gun ownership: Not retained in best-fitting model; no significant effect when included. Epidemic predictors: - Group membership: Strong positive effect; events involving group members are over four times more likely to be followed by spatially/temporally proximate events (RR=4.563; 95% CI: 1.57–13.28; p=0.0054). - Social media role in radicalization: Positive effect; such events are almost three times more likely to be followed by proximate events (RR=2.722; 95% CI: 1.55–4.76; p=0.0005). - Anticipated fatalities and plot success: Not included in best-fitting model (no evidence supporting a copy-cat mechanism via media salience). Model performance: - Simulations closely matched observed cumulative exposures in the final six months and captured spatial patterns (with weighting toward high-density areas).

Findings support the hypothesis that far-right radicalization in the U.S. spreads via a complex contagion process requiring reinforcement rather than a simple copy-cat effect. The significant epidemic component (R0=0.31<1) indicates that while widespread, self-sustaining spread is unlikely, clusters can occur under conducive endemic and epidemic conditions. The strong epidemic effects of group membership and social media imply that activism, organizing, and digitally mediated community engagement drive linkage between events, and that online platforms augment, rather than replace, physical organizing with a geographically biased diffusion. Endemic factors shape baseline risk: higher county-level poverty and greater hate group presence elevate radicalization probability, while higher Republican voting share, larger non-white population, and higher unemployment correlate with lower probabilities. The negative association with percent non-white aligns with intergroup contact hypotheses when controlling for population density. Gun ownership and violent crime do not significantly influence radicalization in this framework, suggesting different drivers from ideologically neutral mass shootings. The decreasing endemic trend over time coupled with episodic spikes (e.g., around national elections) underscores the interaction between macro-political contexts and contagion dynamics. Overall, the results indicate that targeted interventions at points of organizing and online engagement may be effective in disrupting contagion pathways of far-right radicalization.

Far-right radicalization in the United States appears to diffuse as a complex contagion, with reinforcement via extremist group membership and social media use significantly enhancing the likelihood of subsequent local radicalizations. Endemic conditions—particularly higher poverty and greater hate group activity—raise regional risk, whereas higher Republican voting share, higher non-white population proportions, and higher unemployment correlate with lower risk. The epidemic component has become relatively more influential over time. Policy and practice implications include prioritizing resources to counter local organizing and online recruitment, supporting data collection on gun violence and hate crime, and bolstering community diversity and tolerance initiatives. Future research should evaluate specific interventions—such as online counter-narratives and disruption of organizing networks—test causal pathways, improve spatial/temporal data resolution (including individual-level social media histories), and model interactions among socioeconomic factors (e.g., poverty-unemployment dynamics).

- Data coverage: PIRUS represents only a subset of radicalized individuals; potential spatial/temporal biases due to underreporting and variable law enforcement practices. Hate crimes are notably underreported, potentially more so in areas with far-right legacies and police overlap. - Spatial resolution: Event locations geocoded to city-level, which may inflate apparent spatial clustering. - Missing data: Social media involvement missing for 54.8% of individuals; although estimates were robust to multiple imputation, results should be interpreted cautiously. - Covariate resolution: Some endemic predictors available only at state-level (gun ownership, violent crime, hate groups), potentially masking local variation. Gun ownership measured via proxy based on suicides and hunting licenses. - Modeling choices: Alternative spatial/temporal kernels converged to unrealistically steep decays influenced by tie-breaking; step functions used accordingly. Assumption that exposure location approximates radicalization location may not hold for all cases. - External validity: Findings specific to U.S. far-right cases (2005–2017) and may not generalize to other ideologies, countries, or periods with different social-media/platform dynamics.