Cambridge Governance Labs
Political Topology:
How We Measure
Freedom
A Methodology Guide — The quantitative framework, data sources, models, and known limitations behind the Political Topology Index
Political Topology Project · Methodology Series M-11
Data: Freedom House · V-Dem · Fragile States Index · World Bank · UNDP · IMF
February 2026
Section 1
What Is Political Topology?
Political Topology is a quantitative framework that treats political regimes as positions in a phase space — a multi-dimensional coordinate system where each country occupies a measurable location defined by liberty, tyranny, and chaos. Rather than reducing politics to a single left-right spectrum, Political Topology maps the full terrain of governance.
Think of a marble on a contoured landscape. Countries don't float freely — they settle into basins, pulled by gravity-like forces. Democratic institutions create one basin; authoritarian control creates another; state failure creates a third. The shape of the landscape determines where countries end up and how hard it is to move them.
1,656
Country-Year
Observations
Not a Spectrum — a Space
Most indices rank countries on a single axis: more free or less free. This loses critical information. A country with a strong dictator and functioning institutions (Russia) is profoundly different from a country with no effective state at all (Somalia), even if both score low on "freedom." Political Topology captures this difference by placing countries in a three-dimensional space:
Liberty (L)
Political freedom and civil liberties. The presence of meaningful elections, free press, independent judiciary, and protected rights. High L = open society.
Tyranny (T)
State coercive capacity deployed against citizens. Repression, surveillance, political imprisonment. High T = controlled society.
Chaos (C)
State failure, violence, lawlessness. Absence of effective governance in any form. High C = ungoverned society.
This three-part framework reveals the fundamental insight: the opposite of freedom is not just dictatorship — it can also be anarchy. And dictatorships are not the same as failed states. Each requires different analysis, different interventions, and different predictions.
Section 2
The Ternary Constraint
At the mathematical core of Political Topology lies a simple but powerful constraint: for any country at any point in time, the three governance dimensions must sum to 100.
The Ternary Phase Space
Liberty (L)
+
Tyranny (T)
+
Chaos (C)
L + T + C = 100
Every country's governance state is a point on a triangle. More of one dimension necessarily means less of the others. A gain in liberty must come at the expense of tyranny, chaos, or both.
How Each Component Is Measured
| Component | Source | Mapping Method | Range |
|---|
| Liberty (L) |
Freedom House (FIW aggregate score) |
Direct mapping: FH 0–100 scale → L 0–100 |
0–100 |
| Chaos (C) |
Fragile States Index (FSI total score) |
Inverted & rescaled: High fragility → High C |
0–100 |
| Tyranny (T) |
Computed as residual |
T = 100 − L − C |
0–100 |
Why is Tyranny a residual? Liberty and Chaos are measured directly from established, validated indices. Tyranny is computed as the remainder: T = 100 − L − C. This enforces the ternary constraint but means Tyranny is not independently measured. If Freedom House overstates a country's liberty, the model will understate its tyranny, and vice versa. This is a known limitation (see Section 7).
Example: Three Countries in Phase Space
| Country | L (Liberty) | T (Tyranny) | C (Chaos) | Interpretation |
|---|
| Finland | 100 | 0 | 0 | Maximum liberty, minimal coercion, stable state |
| Russia | 13 | 78 | 9 | Low liberty, high state coercion, functioning state |
| Somalia | 5 | 22 | 73 | Near-zero liberty, modest coercion, state failure |
Finland, Russia, and Somalia all score low on liberty. But their political realities are profoundly different — a difference the ternary framework captures and a single "freedom score" cannot.
Section 3
Data Sources
Political Topology draws on six major data sources, each contributing a distinct layer of measurement. No single index captures the full picture; the framework ssynthesises them into a unified phase-space representation.
| Source | Coverage | Countries | Key Variables |
|---|
Freedom House
Freedom in the World |
1972–2025 |
195 |
Political rights + civil liberties aggregate score (0–100). Primary source for Liberty (L). |
V-Dem Institute
Varieties of Democracy |
1789–2024 |
202 |
600+ indicators across electoral, liberal, participatory, deliberative, and egalitarian democracy dimensions. |
Fragile States Index
Fund for Peace |
2006–2024 |
179 |
12 instability indicators (cohesion, economic, political, social). Primary source for Chaos (C). |
World Governance Indicators
World Bank |
1996–2023 |
215 |
6 dimensions: voice & accountability, political stability, government effectiveness, regulatory quality, rule of law, corruption control. |
World Bank / UNDP / IMF
Economic & Development Data |
Various |
190+ |
GDP per capita, life expectancy, education metrics, inequality indices, maternal mortality, infrastructure access. |
How the PTI Differs from Published Indices
Updates faster. Freedom House and V-Dem publish annually, often with a 6–12 month lag. The PTI incorporates real-time institutional signals (judicial rulings, press freedom events, legislative actions) and can update assessments within weeks of significant governance changes.
Weights institutional erosion more heavily. Established indices tend to adjust slowly, giving benefit of the doubt to long-standing democracies. The PTI weights the rate of institutional constraint erosion, not just the current level, detecting acceleration before aggregate scores move.
Can diverge during rapid change. Because of these design choices, PTI scores can diverge significantly from Freedom House, and V-Dem during periods of rapid institutional change. For example, during the US 2024–25 period, published FH scores remained at 83 whilst the PTI assessed the US at 48 — a 35-point gap. The credible range for the US in early 2026 is 48–84, with the truth likely in the 57–70 zone. This divergence is a feature, not a bug: it reflects the PTI's emphasis on leading rather than lagging indicators.
Section 4
The Tristable Basin Model
The central dynamical model in Political Topology treats the liberty landscape as a potential energy surface with three stable basins — regions where countries tend to settle and resist perturbation. This is not a metaphor; it is a formal model derived from Langevin stochastic differential equations fitted to 225 years of regime transition data.
1. Democratic Plateau (L > 80)
31 countries currently reside here. This is a deep, stable basin reinforced by institutional redundancy: independent courts, free press, competitive elections, and civil society all act as sstabilising mechanisms. Recovery from perturbation is ~82%. Think of it as a high plateau — hard to push a marble off the edge. Examples: Finland (100), Norway (98), New Zealand (97), Canada (95), Taiwan (92).
2. Hybrid Trap (L = 20–70)
32 countries here. A shallow, unstable basin — the zone of maximum volatility. Countries oscillate between partial openings and renewed closures. Some hold elections that lack meaning; others have free media but captured courts. The basin is shallow: small shocks can tip countries towards either democracy or tyranny. Examples: Hungary (52), India (62), Mexico (60), Nigeria (43).
3. Tyranny Well (L < 20)
28 countries here. The deepest basin in the landscape — once a country settles here, escape is near-impossible without extraordinary intervention. The state controls all levers: media, courts, military, economy. Recovery rate: approximately 3.0% (95% CI: 0.7–6.0%). Examples: China (5), Russia (13), Saudi Arabia (7), North Korea (2), Iran (12).
The Event Horizon: L ≈ 52–55
This is the Critical Instability Zone. Below this threshold, the probability of self-correction collapses. Three independent methods converge on this range:
- Survival analysis of regime transitions
- Markov transition probability matrices
- Langevin SDE potential landscape estimation
Below the event horizon: recovery probability = 3.0% (95% CI: 0.7–6.0%)
Evidence: How Do We Know?
The three-basin structure is not assumed — it is estimated from the data using Gaussian Mixture Models (GMM, K=3). Markov transition matrices confirm that countries move between basins with asymmetric probabilities: the transition from "Hybrid" to "Tyranny" (downward) is approximately four times more likely than the transition from "Hybrid" to "Democracy" (upward). The Langevin SDE potential landscape provides a continuous version of the same finding: the potential surface has three distinct minima separated by energy barriers of unequal height.
Section 5
The Eight-Step Erosion Model
How do democracies die? Not suddenly — incrementally. The Eight-Step Erosion Model describes the typical sequence by which a functioning democracy degrades into autocracy. Each step is individually defensible by the regime; collectively, they dismantle democratic governance.
1
Norm Erosion
Informal democratic norms (restraint, respect for precedent, bipartisan cooperation) are violated without formal rule-breaking. The guardrails weaken before the structure collapses.
2
Information Capture
Independent media is delegitimized, co-opted, or replaced. State-aligned narratives dominate. The public loses the ability to form informed judgments about governance.
3
Judicial Capture — THE EVENT HORIZON
Courts lose independence and become instruments of executive power. This is the critical threshold: once the judiciary cannot check the executive, all subsequent steps become dramatically easier. Recovery probability collapses.
4
Legislative Subordination
The legislature becomes a rubber stamp. Opposition is mmarginalised through procedural manipulation, party discipline, or intimidation. Laws are passed to consolidate executive power.
5
Regulatory Capture
Independent agencies (central banks, election commissions, anti-corruption bodies) are staffed with loyalists. The administrative state serves the regime, not the public.
6
Civil Society Suppression
NGOs, unions, universities, and civic oorganisations are defunded, harassed, or banned. The oorganised opposition that could mobilize resistance is dismantled.
7
Electoral Manipulation
Elections continue but are no longer meaningful. Gerrymandering, voter suppression, media monopoly, and opposition disqualification ensure regime continuity.
8
Constitutional Consolidation
The regime rewrites the constitution or amends it to entrench power permanently. Term limits are removed. Emergency powers become permanent. The autocratic transition is legally complete.
Key insight: Steps 1–2 are reversible with moderate effort. Step 3 (judicial capture) is the inflection point. Steps 4–8 occur with accelerating speed and diminishing resistance. The model predicts that once Step 3 is complete, the median time to reach Step 6 is approximately 3–5 years.
Section 6
The Human Capabilities Index (HCI)
Political freedom is one dimension of human flourishing, but not the only one. The Human Capabilities Index measures whether states deliver the material conditions for a dignified life, regardless of regime type. It is grounded in the Sen-Nussbaum Capability Approach: freedom means nothing if people lack the health, education, and resources to exercise it.
4
Indicators
Complete (27%)
3,479
Data Points
Collected
The Seven Capability Domains
1. Survival & Longevity
Life expectancy, mortality rates. Can citizens expect to live a full life?
2. Maternal & Child Health
Maternal mortality, neonatal survival, child nutrition. Are the most vulnerable protected?
3. Knowledge & Education
Literacy, years of schooling, educational quality. Can citizens develop their minds?
4. Material Living Standard
Income, poverty rates, inequality. Can citizens meet their basic material needs?
5. Psychological Well-being
Mental health, life satisfaction, social connection. Can citizens live without despair?
6. Basic Infrastructure
Clean water, sanitation, electricity, internet access. Do the systems of daily life function?
7. Agency & Equality
Gender equality, minority rights, access to justice. Can all citizens participate as equals?
Completion Status
4 of 15 indicators operational (27%). Target: 15 of 15 by end of 2026.
Data ethics commitment: "No interpolation. No fabrication. Missing = blank." When a data point is unavailable for a country-year, the HCI records it as missing rather than estimating it. We believe that honest gaps are more useful than confident fictions. Users of our data will always know what we measured and what we did not.
Section 7
Known Limitations
No framework is perfect. We believe that acknowledging limitations openly is more valuable than concealing them. The following are the most significant weaknesses of the current Political Topology methodology.
1
Tyranny measured as residual
Tyranny (T) is not independently measured. It is computed as T = 100 − L − C, making it dependent on the accuracy of both the Liberty, and Chaos measurements. If Freedom House overstates a country's liberty, the model will systematically understate its tyranny. Future versions should incorporate independent tyranny indicators (e.g., political prisoner counts, surveillance metrics, extrajudicial violence data).
2
PTI can diverge from established indices
During rapid institutional change, the PTI's emphasis on leading indicators can produce scores that diverge significantly from Freedom House and V-Dem. The US case (PTI: 48, FH: 83) is the most dramatic example. These divergences may reflect the PTI's greater sensitivity to recent events — or they may reflect overreaction. Time will tell which assessments prove more accurate.
3
Python standard library only
All statistical analysis is performed using Python's standard library. No scipy, statsmodels, or other third-party statistical packages are used. This is a deliberate audit constraint — every line of code is inspectable and self-contained — but it limits the sophistication of available statistical methods and may introduce implementation differences from reference algorithms.
4
Small N for US-specific claims
The US has 13 observations over 225 years in the dataset. Claims about US-specific trajectories, velocities, and transition probabilities are based on this small sample. Statistical confidence intervals are wide. Cross-country comparisons provide supporting evidence but cannot substitute for a larger US-specific sample.
5
67% crosswalk match with Freedom House
When PTI Liberty scores are compared to Freedom House aggregate scores, the crosswalk match rate is 67%. This means one-third of country-years show non-trivial divergence. Some divergence is by design (the PTI weights different signals), but 33% disagreement with the field's standard-bearer demands ongoing investigation and calibration.
6
AR(1) outperforms stage models
A simple first-order autoregressive model (next year's Liberty score = this year's score + noise) outperforms the eight-stage erosion model in out-of-sample prediction. This is a humbling finding: simplicity may beat complexity. The stage model's value may lie more in explanation and communication than in raw predictive accuracy.
Our approach: We publish these limitations because we believe that transparent methodology is more trustworthy than polished methodology. Every framework has weaknesses. The question is whether those weaknesses are hidden or disclosed.
Section 8
Open Data and Replication
Political Topology is fully open. Every data point, every script, every methodological choice is available for inspection, replication, and critique. We do not ask anyone to trust our conclusions — we ask them to check our work.
26
Python Replication
Scripts
What We Provide
Complete Dataset
All country-year observations in both XLSX and CSV format. Every variable, every source, every transformation documented. No proprietary formats, no access restrictions. Download, aanalyse, disagree.
Replication Scripts
26 Python scripts covering every analytical step: data ingestion, variable construction, ternary calculation, basin estimation, transition matrices, erosion staging, and all vvisualisations. Python standard library only — no dependencies to install.
Full Documentation
A complete replication README that walks through every step from raw data to final output. Variable definitions, mapping decisions, edge cases, and the reasoning behind every methodological choice.
Limitations and Mistakes
We publish not only our results but also our known limitations, our calibration failures, and our disagreements with established indices. If we got something wrong, the data to prove it is freely available.
Replication invitation: If you are a researcher, journalist, or student, and you find an error in our data, our code, or our analysis, we want to hear from you. The entire point of open methodology is that it can be corrected. Contact us at the address below.
We built this framework because existing measures of political freedom — while valuable — lacked the dynamical perspective needed to understand how democracies erode, not just whether they are eroding. Political Topology is a work in progress. We publish our data, our code, our methodology, and our mistakes.