1 Indices Analysis

The study use three political extremism indices to examine how various types of destabilizing events differently affect population groups with different political affiliations (left-wing, center-wing, right-wing), thereby increasing or decreasing their political extremism score.

The hypotheses we test are:

  • H1: Various dimensions of political extremism do not respond uniformly to socio-political events.
  • H2: The effect of different destabilizing events will be moderated by political orientation.

We use the following political extremism indices:

  • Extremism Levels (EL) – Percentage of the population identified as the more extremist group.
  • Extremism Intensity (EIN) – Mean political extremism score of the population identified as the more extremist group.
  • Extremism Rank 3 (ER3) – Percentage of the population with all three political extremism dimension scores higher than the threshold for defining the more extremist group.

We calculated the scores of the three indices across six survey waves. Destabilizing events occurred between each two consecutive events: Inland Terror (w1-w2), Bennet Gov. Fall (w2-w3), Judicial Reform (w3-34), Gallant Dismissal (w4-w5), and the Oct. 7th War (w5-w6).

community_variable <- "pe_left_center_right"
community_order <- c("left", "center", "right")

wave_order <- c("First", "Second", "Third", "Fourth", "Fifth", "Sixth")
dimensions_order <- c("Overall", "Cognitive", "Behavioral", "Social")
wave_transition_order <- 
  c("First-Second", "Second-Third", "Third-Fourth", "Fourth-Fifth", "Fifth-Sixth")

# Read the data from indices_table.txt
df <- as.data.frame(readRDS("Israel Survey/data/il_pe.RDS"))
indices_df <- af_gauge_indices(df, pop_var1 = "Wave", comm_var1 = community_variable, 
                               threshold_type = "MAD", k_factor = 1.5)
indices_data <- indices_df$indices_table

# Convert data to a more manageable format for analysis

df <- indices_data %>%
  mutate(Wave = factor(Wave, levels = wave_order)) %>%
  mutate(!!sym(community_variable) := factor(!!sym(community_variable), levels = community_order))
         
# Separate the data into population and community data
pop_data <- df %>% filter(is.na(!!sym(community_variable)))
community_data <- df %>% filter(!is.na(!!sym(community_variable)))

1.1 Results

plot_data <- community_data

# Extremism Levels 

plot_data <- community_data

p1 <- af_create_xy_plot(data = plot_data, x_var = "Wave", y_var = "cel_c",
                        grouping_variable = community_variable, show_points = TRUE,
                        title = "Extremism Level (EL): Cognitive Dimension",
                        y_label = "EL Score %", legend_position = "right", legend_label = "") +
  scale_x_discrete(limits = levels(df$Wave))
p_el1 <- af_event_labels(p1)

p2 <- af_create_xy_plot(data = plot_data, x_var = "Wave", y_var = "bel_c",
                        grouping_variable = community_variable, show_points = TRUE,
                        title = "Extremism Level (EL): Behavioral Dimension",
                        y_label = "EL Score %", legend_position = "right", legend_label = "") +
  scale_x_discrete(limits = levels(df$Wave))
p_el2 <- af_event_labels(p2)

p3 <- af_create_xy_plot(data = plot_data, x_var = "Wave", y_var = "sel_c",
                        grouping_variable = community_variable, show_points = TRUE,
                        title = "Extremism Level (EL): Social Dimension",
                        y_label = "EL Score %", legend_position = "right", legend_label = "") +
  scale_x_discrete(limits = levels(df$Wave))
p_el3 <- af_event_labels(p3)

# Extremism Intensity

p1 <- af_create_xy_plot(data = plot_data, x_var = "Wave", y_var = "cin_c",
                        grouping_variable = community_variable, show_points = TRUE,
                        title = "Extremism Intensity (EIN): Cognitive Dimension",
                        y_label = "EIN Score", legend_position = "right", legend_label = "") +
  scale_x_discrete(limits = levels(df$Wave))
p_ein1 <- af_event_labels(p1)

p2 <- af_create_xy_plot(data = plot_data, x_var = "Wave", y_var = "bin_c",
                        grouping_variable = community_variable, show_points = TRUE,
                        title = "Extremism Intensity (EIN): Behavioral Dimension",
                        y_label = "EIN Score", legend_position = "right", legend_label = "") +
  scale_x_discrete(limits = levels(df$Wave))
p_ein2 <- af_event_labels(p2)

p3 <- af_create_xy_plot(data = plot_data, x_var = "Wave", y_var = "sin_c",
                        grouping_variable = community_variable, show_points = TRUE,
                        title = "Extremism Intensity (EIN): Social Dimension",
                        y_label = "EIN Score", legend_position = "right", legend_label = "") +
  scale_x_discrete(limits = levels(df$Wave))
p_ein3 <- af_event_labels(p3)

# Extremism Rank 3

p3 <- af_create_xy_plot(data = plot_data, x_var = "Wave", y_var = "er3_c",
                        grouping_variable = community_variable, show_points = TRUE,
                        title = "Extremism Rank 3 (ER3)",
                        y_label = "ER3 Score %", legend_position = "right", legend_label = "") +
  scale_x_discrete(limits = levels(df$Wave))
p_er3 <- af_event_labels(p3)
# Combined Plot

plot_list <- list(p_el1, p_el2, p_el3, p_ein1, p_ein2, p_ein3, p_er3)
af_combine_plots (plot_list, ncol = 1, 
                  main_title = "", 
                  subtitle = NULL, note = NULL, common_legend = FALSE,
                  legend_position = "right", external_legend = NULL, legend_labels = NULL,
                  row_spacing = 0.1, col_spacing = 0.1)

1.2 Interpretation

The longitudinal analysis reveals substantial heterogeneity in political extremism trajectories across the five destabilizing events, with marked variations between dimensions, political orientation groups, and between extremism levels and intensity measures. Following the Inland Terror attack, extremism levels showed mixed patterns—right-wing social extremism increased from 22.64% to 26.27% while left-wing behavioral extremism dropped from 32.92% to 20.00%—yet extremism intensity remained relatively stable across dimensions, with cognitive intensity declining modestly from 6.81 to 6.41 among left-wing respondents. The fall of the Bennett Unity Government triggered the most pronounced cognitive extremism surge among left-wing respondents (34.29% to 60.38%) while maintaining stable intensity levels (6.41 to 6.34), suggesting broader radicalization without deepening commitment among existing extremists. The Judicial Reform period sustained elevated left-wing cognitive extremism (57.30%) while driving all groups’ cognitive intensity to their lowest points (left: 6.34, center: 6.10, right: 6.13), indicating widespread but shallow ideological polarization. Conversely, this period eliminated left-wing social extremism entirely (2.83% to 0.00%) yet maintained stable social intensity (6.57). The Galant Dismissal reversed left-wing cognitive extremism levels (57.30% to 33.71%) while slightly increasing cognitive intensity (6.36 to 6.54), suggesting consolidation among remaining extremists. The October 7th war generated the most comprehensive escalation, with left-wing behavioral extremism peaking at 39.52% accompanied by a dramatic intensity surge from 2.44 to 3.00—the highest behavioral intensity recorded. The composite ER3 measure showed right-wing comprehensive extremism declining consistently from 3.77% to 1.06%, while left-wing and center-wing ER3 remained near zero throughout most waves before modest increases in the final period (0.81% and 0.61% respectively).

1.3 Discussion

The empirical findings provide robust support for both hypotheses, demonstrating clear dimensional heterogeneity (H1) and political orientation moderation effects (H2) in extremism responses to destabilizing events. Evidence for H1 is particularly striking in the differential dimensional responses within the same political groups: during the Bennett Government’s fall, left-wing respondents exhibited a massive cognitive extremism surge (34.29% to 60.38%) while simultaneously experiencing continued behavioral extremism decline (20.00% to 17.92%), and during the October 7th crisis, left-wing behavioral extremism peaked at 39.52% with unprecedented intensity escalation (2.44 to 3.00) while cognitive increases were more moderate (33.71% to 48.39%) with stable intensity (6.54 to 6.69). The social dimension demonstrated the most distinct trajectory, remaining consistently low among left-wing respondents and even disappearing entirely during the Judicial Reform period, contrasting sharply with right-wing social extremism’s persistent elevation (consistently above 20%). Support for H2 emerges through systematically opposite responses across political orientations to identical events: the Judicial Reform period drove center-wing cognitive extremism from 12.18% to 21.69% while right-wing cognitive extremism remained stable (16.61% to 16.71%), and the Galant Dismissal triggered a dramatic left-wing cognitive extremism collapse (57.30% to 33.71%) concurrent with right-wing behavioral extremism increases (27.68% to 30.15%). Most compelling is the contrasting ER3 comprehensive extremism trajectories, with right-wing composite extremism declining steadily from 3.77% to 1.06% across all events, while left-wing and center-wing ER3 measures remained near zero until modest final-wave increases, suggesting fundamentally different extremism consolidation patterns across the political spectrum that persist regardless of event type.

The extremism intensity analysis reveals that while political events dramatically influence the proportion of citizens embracing extremist positions (extensive margin), they have minimal impact on the severity of beliefs among already radicalized individuals (intensive margin), providing crucial insights that complement the extremism levels findings. Across all dimensions, intensity variations remain remarkably compressed—cognitive intensity ranges of only 0.47-0.78 points despite 26-percentage-point level fluctuations, and social intensity variations of merely 0.18-0.38 points—indicating that extremism operates primarily through recruitment and demobilization mechanisms rather than progressive belief intensification. The notable exception occurs in left-wing behavioral intensity, which increases 0.56 points following October 7th (from 2.44 to 3.00), suggesting that while most extremism dimensions function through binary activation processes, external security threats may uniquely deepen violence-oriented inclinations among progressive extremists. These patterns demonstrate that the dramatic extremism level changes identified earlier reflect shifts in extremist constituency size rather than radicalization depth, indicating that political events mobilize latent attitudes rather than progressively radicalizing moderate positions, with important implications for understanding how crises expand rather than intensify extremist movements.

We consider a threat-based mechanism, positing that destabilizing events differentially affect political extremism based on the perceived threat level to each political orientation group: events threatening specific political constituencies should heighten extremism within those groups while reducing extremism among groups perceiving diminished threats. This framework predicts that Inland Terror and October 7th would universally increase extremism given their broad societal threat, while partisan events like the Bennett Government’s fall and Judicial Reform would increase left-wing/center extremism but decrease right-wing extremism, and the Galant Dismissal would produce opposite effects. The empirical evidence provides mixed support for this mechanism. The strongest validation emerges from the Bennett Government’s collapse, where left-wing cognitive extremism surged dramatically (34.29% to 60.38%) while right-wing extremism declined across dimensions, precisely matching theoretical predictions. October 7th also aligns well with universal threat predictions, generating comprehensive extremism increases including unprecedented left-wing behavioral intensity (2.44 to 3.00) and notable ER3 composite increases for left-wing (0.00% to 0.81%) and center-wing (0.00% to 0.61%) groups. However, the mechanism faces challenges with other events: Inland Terror failed to produce universal increases, with left-wing behavioral extremism declining substantially (32.92% to 20.00%), and the Galant Dismissal generated more complex patterns than predicted, with dramatic left-wing cognitive collapse (57.30% to 33.71%) rather than gradual decline.

These mixed results suggest that while threat perception influences extremism responses, additional factors including aggregated effects of events or additional moderators such as event salience might moderate the relationship between perceived threats and extremist mobilization across political orientation groups.

1.4 Detailes Results (For SI)

# Extremism Levels

af_create_xy_table(df = plot_data, x_var = "Wave", y_var = "cel_c", g_var = community_variable,
                   title = "Extremism Level (EL): Cognitive Dimension")
Extremism Level (EL): Cognitive Dimension
pe_left_center_right First Second Third Fourth Fifth Sixth
left 34.16 34.29 60.38 57.30 33.71 48.39
center 12.93 9.89 12.18 21.69 15.97 24.39
right 21.98 17.70 16.61 16.71 13.72 16.16
 
af_create_xy_table(df = plot_data, x_var = "Wave", y_var = "bel_c", g_var = community_variable,
                   title = "Extremism Level (EL): Behavioral Dimension")
Extremism Level (EL): Behavioral Dimension
pe_left_center_right First Second Third Fourth Fifth Sixth
left 32.92 20.00 17.92 29.21 33.15 39.52
center 30.39 24.00 28.99 31.22 30.63 38.72
right 39.62 38.56 35.79 27.68 30.15 27.79
 
af_create_xy_table(df = plot_data, x_var = "Wave", y_var = "sel_c", g_var = community_variable, 
                   title = "Extremism Level (EL): Social Dimension")
Extremism Level (EL): Social Dimension
pe_left_center_right First Second Third Fourth Fifth Sixth
left 2.88 3.67 2.83 0.00 2.81 4.84
center 10.56 6.53 7.56 8.99 8.32 8.54
right 22.64 26.27 20.30 22.43 21.15 21.15
 

# Extremism Intensity

af_create_xy_table(df = plot_data, x_var = "Wave", y_var = "cin_c", g_var = community_variable,
                   title = "Extremism Intensity (EIN): Cognitive Dimension")
Extremism Intensity (EIN): Cognitive Dimension
pe_left_center_right First Second Third Fourth Fifth Sixth
left 6.81 6.41 6.34 6.36 6.54 6.69
center 6.70 6.32 6.10 6.09 6.44 6.50
right 6.91 6.31 6.13 6.25 6.73 6.45
 
af_create_xy_table(df = plot_data, x_var = "Wave", y_var = "bin_c", g_var = community_variable,
                   title = "Extremism Intensity (EIN): Behavioral Dimension")
Extremism Intensity (EIN): Behavioral Dimension
pe_left_center_right First Second Third Fourth Fifth Sixth
left 2.09 2.39 2.21 2.37 2.44 3.00
center 2.52 2.77 2.54 2.68 2.68 2.55
right 2.39 2.75 2.67 2.64 2.73 2.67
 
af_create_xy_table(df = plot_data, x_var = "Wave", y_var = "sin_c", g_var = community_variable, 
                   title = "Extremism Intensity (EIN): Social Dimension")
Extremism Intensity (EIN): Social Dimension
pe_left_center_right First Second Third Fourth Fifth Sixth
left 6.19 6.22 6.57 NaN 6.30 6.38
center 6.20 6.08 6.46 6.29 6.37 6.33
right 6.31 6.28 6.44 6.30 6.42 6.26
 

# Extremism Rank 3

af_create_xy_table(df = plot_data, x_var = "Wave", y_var = "er3_c", g_var = community_variable,
                   title = "Extremism Rank 3 (ER3)")
Extremism Rank 3 (ER3)
pe_left_center_right First Second Third Fourth Fifth Sixth
left 0.41 0.41 0.00 0.00 0.00 0.81
center 0.43 0.21 0.00 0.53 0.00 0.61
right 3.77 4.17 3.14 2.86 1.57 1.06