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Cambridge Governance Labs (CGL) is a research initiative applying quantitative methods to the study of democratic transitions and governance quality. The Political Topology project is our flagship research program, combining 225 years of historical data with modern statistical methods to map the physics of political change.
Political Topology is a quantitative framework that models political systems as a tristable attractor landscape. It describes how countries cluster around three stable equilibria — democracy, hybrid regimes, and tyranny — and maps the transition dynamics between them using 225 years of data across 91 countries.
ModelInteractive See the Tristable Attractor Theory overview and the Interactive Explorer.
For press inquiries, research collaboration, or data access requests, contact [email protected]. Visit the About page for more details.
All CGL data is provided under a Creative Commons Attribution 4.0 (CC-BY-4.0) license. You are free to share and adapt the data for any purpose, provided you cite Cambridge Governance Labs. See the Data Downloads page.
Yes. The Press Kit page provides brand assets, key findings summaries, and media-ready materials for journalists and researchers.
Political systems are not random — they cluster around three stable equilibria, like marbles settling into wells in a landscape. The model identifies these three "attractor basins" and maps the dynamics of how countries move between them.
Interactive Explore the Basin Overview visualization to see the tristable landscape in action.
The model identifies three zones of political stability, validated by Gaussian Mixture Model analysis (BIC-optimal K=3):
Interactive See the Stability Wells visualization and Attractor Basin Map.
Democratic erosion follows a predictable eight-stage sequence, from early institutional stress through to autocratic consolidation. The key insight: the sequence includes a critical branching point at the Hybrid Trap where outcomes diverge — countries either recover or accelerate toward tyranny.
Interactive The Eight Stages visualization maps stage duration and momentum for each transition.
Political power operates under a conservation constraint: Liberty + Tyranny + Chaos = 100. Power doesn't disappear — it redistributes. When institutional liberty declines, that power flows either to autocratic consolidation (tyranny) or to disorder (chaos). This constraint defines the topology of the political phase space.
Escape velocity is the minimum momentum a country needs to break free from one attractor basin and transition to another. The Tyranny Well has the deepest walls, requiring the most force to escape. The model maps intervention points where external or internal pressure is most effective.
Interactive See the Escape Velocity and Intervention Points visualizations.
The Complete Integrated Model page combines all components — three basins, eight stages, escape velocity, and conservation law — into a single interactive visualization, alongside the empirical basin validation.
ModelInteractive
The Thesis Architecture page presents a comprehensive interactive synthesis showing how every claim, piece of evidence, and statistical test connects across the full Political Topology project. It serves as a navigational map of the research structure.
Interactive
The liberty score (L) is a 0–100 composite index produced by the Political Topology Index (PTI), which draws primarily on Freedom House data with cross-validation against V-Dem and other democracy indices. The PTI updates more frequently than published annual indices and weights institutional constraint erosion more heavily, so it may diverge from published FH or V-Dem scores. It quantifies institutional quality: judicial independence, press freedom, electoral integrity, civil liberties, and checks on executive power. Higher scores = greater liberty.
Data The full dataset covering 91 countries from 1800–2025 is available on the Data Downloads page.
The Hybrid Trap (L ≈ 57) is a shallow but persistent attractor basin where countries hold elections but institutions are captured by ruling elites. It is the most volatile and dangerous zone — small shocks can push a country toward either democracy or tyranny. 32 countries are currently trapped here. Think Turkey, Hungary, or India.
The event horizon (L ≈ 49–55) is the critical instability zone where democratic erosion becomes very difficult to reverse. Three independent methods converge on this range. Countries that cross below this threshold face accelerating institutional decay with diminishing prospects for recovery.
Map See the Critical Instability Zone Map for a global view of which countries are near this boundary.
Velocity measures the rate and direction of change in a country's liberty score over time. Negative velocity indicates democratic erosion; positive velocity indicates democratic recovery. The model tracks both current velocity and acceleration (whether erosion is speeding up or slowing down).
Map The Velocity & Decline map visualizes which countries are eroding fastest.
Think of a landscape with valleys and hills. A ball placed on this landscape will roll downhill and settle in a valley — that's an attractor basin. Each valley represents a stable political configuration (democracy, hybrid, or tyranny). Moving from one valley to another requires enough force to push over the ridge between them. Deeper valleys are harder to escape.
Interactive The Stability Wells visualization renders this landscape in 3D.
Capable autocracies are countries that achieve high governance effectiveness and human development outcomes despite low liberty scores. They represent a decoupling of capability from liberty — demonstrating that material prosperity alone does not prevent or reverse autocratic consolidation.
Map Explore the Capable Autocracies map.
The HCI is a composite index of 15 indicators across 7 domains (health, education, economic security, infrastructure, etc.) for 91 countries. It measures what a state delivers to its citizens independently of political liberty — allowing the model to test whether capability predicts democratic trajectory.
Data Download the full HCI dataset from the Data Downloads page.
The Great Decoupling describes the phenomenon where liberty and capability diverge: some countries achieve high human development while suppressing political freedom, challenging the assumption that prosperity inevitably leads to democracy. A full paper and one-page summary are available on the Downloads page.
The site includes 239 interactive artifacts across multiple categories:
Start with the Maps & Data hub or the Interactive Explorer.
The Global Liberty Index 2025 is a choropleth map of liberty scores across 91 countries. Color coding reflects basin membership: green (democratic plateau), amber (hybrid trap), red (tyranny well). Hover for country details; click for full profiles.
MapInteractive
The Attractor Basin Map classifies all 91 countries by their current basin membership — Democratic Plateau, Hybrid Trap, or Tyranny Well — based on their liberty score and trajectory. The Three Basins page also includes a country grid visualization.
Map
The Critical Instability Zone map highlights countries near the L ≈ 49–55 event horizon. These nations are at greatest risk of irreversible democratic erosion.
Map
The Population-Weighted map rescales the data by population, showing how many people (not just countries) live under each governance type. This reveals that the majority of the world's population lives in hybrid or autocratic regimes, even though the country count appears balanced.
Map
The Synthesis Map combines multiple analytical dimensions into a single integrated visualization — liberty scores, velocity, basin membership, and instability risk — providing the most comprehensive single view of the global political landscape.
MapInteractive
The Interactive Explorer is the full-featured data tool that lets you explore all analytical dimensions: compare countries, filter by region or basin, view historical trajectories, and examine the relationships between liberty, capability, and credit risk. It is the most powerful single entry point into the data.
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The model covers 91 countries with full time-series data, and the site features 95 country timeline profiles. Each profile includes current position, historical trajectory, velocity analysis, stage classification, and probability projections.
Country Browse from the Country Profiles hub, or search for a specific country in the Interactive Explorer.
Under the PTI the US currently scores L≈48 (Stage 5), with a velocity of −18/yr — indicating rapid democratic erosion. Published indices score higher (Freedom House: 83, V-Dem: 65–72); the divergence reflects the PTI's faster update cycle and heavier weighting of institutional constraint erosion. The model identifies the PTI score as below the event horizon. Part 5 of the Sovereign Spread series, The American Exception, examines why US markets have not yet priced this risk.
Country Full profile at US Country Profile.
China scores L=9 (Stage 8) — deep in the Tyranny Well. It is classified as a capable autocracy, achieving high human development outcomes while maintaining near-total political control.
Country See the China profile and Capable Autocracies map.
India scores L=62 and sits near the critical instability zone. Its trajectory shows declining liberty scores, placing it in a precarious position where further erosion could push it firmly into the Hybrid Trap.
Country See the India profile.
Three regional deep dives examine democratic trajectories across key geopolitical zones:
MapCountry
Yes. The Comparative Trajectories page lets you view how different countries' paths have diverged or converged over time. The Interactive Explorer also supports multi-country comparison.
CountryInteractive
The Sovereign Spread: How Credit Markets Price the Death of Democracy is a five-part investigation into the relationship between liberty erosion and sovereign bond yields. The central finding: markets systematically underprice autocratic risk until it is too late.
Credit Read the full series starting from The Sovereign Spread.
CreditInteractive Each part includes interactive visualizations.
The model finds a statistically significant relationship between declining liberty scores and rising sovereign bond spreads. The effect is non-linear: markets remain relatively calm during early erosion stages but reprice sharply when countries cross the event horizon. The yield model controls for GDP per capita and other macroeconomic factors.
Credit See the Credit Market Note for the quantitative details.
The Governance & Economics page examines the broader relationship between institutional quality and economic performance — including cases where autocratic regimes achieve growth (capable autocracies) and where democratic erosion precedes economic decline.
CreditInteractive
The primary data source is Freedom House (1973–2025), cross-validated against V-Dem and other democracy indices. Historical extension to 1800 uses a crosswalk methodology validated in the audit. The full dataset covers 91 countries across 225 years.
DataMethod See the Methodology section for full documentation.
The model is validated through multiple independent methods:
Method All scripts are in the Replication Package.
Yes. The thesis underwent a comprehensive 4-phase audit with 25 fixes applied, raising the overall score from 5.7 to 8.3 out of 10. Six peer review documents cover every layer of the project — from data integrity to statistical methods to narrative claims.
MethodInteractive See the Peer Review & Audit page for the full diagnostic.
Yes. The complete Replication Package includes all Python scripts (3.10+, standard library only) organized by research phase. The package includes foundation audits, model hardening, bootstrap analyses, and validation tests. Download instructions and a README are included.
DataMethod
All datasets are available on the Data Downloads page:
Documents and presentations (methodology DOCX, eight-step model, Great Decoupling paper and slides) are also available.
Data
The audit includes explicit Freedom House methodology sensitivity analysis by era, testing whether scoring changes affect the model's conclusions. The IRT measurement robustness check (ordinal-to-interval conversion) further validates that the results hold across different measurement approaches.
Method See the replication scripts b10_fh_sensitivity.py and c7_irt_measurement.py.
A full uncertainty propagation audit covers 53 claims in the thesis. The model uses bootstrap confidence intervals (1,000–10,000 resamples), Monte Carlo calibration against OECD peer volatility, and credible ranges for all key parameters. The audit explicitly identifies which claims have narrow vs. wide uncertainty bands.
Method See c10_uncertainty_audit.py in the Replication Package.
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