Probability Cone: US Trajectories 2026-2040

Editorial Note: This document separates empirical findings from normative assessment. Policy implications and advocacy statements are collected in the dedicated section at the end.

⚠️ METHODOLOGY NOTE — PTI SCORE DIVERGENCE

The starting position of L=48 reflects the author's PTI (Political Topology Index), a real-time institutional assessment incorporating executive action pace through early 2026. Published indices score the US higher: Freedom House 83/100 (2024 report), V-Dem LDI ~0.65-0.72 (~65-72 scaled). The divergence reflects (a) the PTI's faster update cycle, (b) weighting toward institutional constraint erosion, and (c) incorporation of events post-dating published index coverage. Under Freedom House scoring (L=83), the US starts firmly in the democratic plateau and the probability cone would show recovery toward L*=80.9 with minimal risk of crossing any instability threshold. All probability cone projections are conditioned on the PTI starting position and should be re-evaluated under published index scores. See Sensitivity Analysis below.

Starting Position

L=48 (Feb 2026)

AR(1) Model

α=3.56, β=0.956, L*=80.9

Volatility (data-driven)

σ = 0.45–4.45 by stage

Simulation Runs

N=10,000 · seed=42

Scenario	Percentile Range	2040 Score	Probability	Trigger Conditions
Recovery Best 10% of outcomes	p90 – p95	L = 75	10%	Strong institutional recovery; elections produce alternation; mean reversion dominates. Elite defection, economic crisis forcing reform, sustained mass mobilization.
Stabilization Gradual mean reversion	p50 – p75	L = 67	25%	Institutions hold; gradual mean reversion toward L*=80.9; modest improvement. Judicial independence maintained, federal system holds.
Continued Erosion Slow decline persists	p25 – p50	L = 63	25%	Current trajectory slows but continues; decline at reduced velocity. Partial institutional capture continues; opposition weakened but not eliminated.
Accelerated Decline Worst 10% of outcomes	p5 – p10	L = 52	10%	Worst case under data-driven σ; still above L=50 (no tyranny). Constitutional crisis, military politicization, full judicial capture.

MODEL METHODOLOGY (Phase 5 Recalibration)

AR(1) Model: L(t+1) = 3.56 + 0.956 · L(t) + σ_stage · ε, where ε ~ N(0,1). Calibrated on Freedom House historical data. This model outperforms all stage-based transition models (ΔAIC > 300, Phase 2).
Equilibrium: L* = α / (1 − β) = 80.9. Mean reversion is the dominant dynamic under the FH-calibrated model.
Starting position: L=48 is the PTI (Political Topology Index) assessment. Under Freedom House (L=83), the US starts firmly in the democratic plateau and projections would show correspondingly lower risk.
Data-driven σ: Stage-specific volatility computed from 1,656 Freedom House observations across 91 countries. Values range from 0.45 (Stage 1) to 4.45 (Stage 7). Thesis stipulated σ (3–7) were 2–7× too high and are SUPERSEDED.
Bounds: L clamped to [0, 100]. N = 10,000 paths, random.seed(42).
Source:phase5-recalibrated-monte-carlo.py (Phase 5 replication package).

Volatility Calibration Sensitivity

Monte Carlo projections are highly sensitive to the choice of calibration peer group. The AR(1) model is calibrated on Freedom House data. The following table compares results under four different volatility assumptions, all starting at L=48 (PTI). Under Freedom House scoring (L=83), these projections would be fundamentally different — the US would start near equilibrium.

Calibration Group	Sigma	Drift	P(L<30 \| 5yr)	P(L>55 \| 5yr)	Median 5yr	Median 10yr
OECD Democracies (25 countries)	3.78	+0.571	0.6%	12.9%	50.4	53.2
All Democracies (39 countries, recent L>70)	3.50	+0.523	0.5%	10.9%	50.2	52.8
Declining Democracies (43 countries, -10pt drop)	3.05	+0.131	0.4%	5.2%	48.3	48.9
Turkey/Venezuela/Hungary (3 countries) *	3.42	-0.207	1.5%	4.6%	46.6	45.5

* Highlighted row indicates the calibration used in the main probability cone above. 1,000 Monte Carlo paths, 10-year horizon.

Interpretation: Volatility (sigma) is comparable across peer groups (OECD: 3.78, Turkey/Ven./Hungary: 3.42). The critical difference is drift: OECD democracies average +0.57 pts/yr (slight upward tendency) vs. -0.21 pts/yr for Turkey/Venezuela/Hungary (negative drift embeds a declining trajectory assumption). Under OECD calibration, P(L<30 within 5 years) = 0.6% and the median 10-year outcome is L=53 (vs. L=45 under thesis calibration). The choice of calibration peer group -- particularly its drift parameter -- is the single largest driver of projection differences. Readers should evaluate which peer group best represents the US trajectory.

MODEL SUMMARY (Phase 5 Recalibrated)

With data-driven σ and FH-calibrated AR(1) mean reversion, the median 15-year trajectory from the PTI starting point of L=48 is L=65 (Democratic Erosion zone), not L=8 as the original thesis projected. P(L<25 by 2040) ≈ 0%. Even the 5th percentile (worst case) remains above L=52. The probability cone is dramatically narrower than the original: the 95% CI spans L=52–75 at 2040, compared to L=2–82 under thesis σ. The original P(tyranny)=62% claim is retracted; it was driven by stipulated σ values 2–7× higher than empirical estimates. Mean reversion toward L*=80.9 is the dominant dynamic. Note: the PTI-measured velocity (−7.6/yr) falls ~3σ outside this FH-calibrated model, reflecting a measurement divergence between indices. See Policy Implications below for normative assessment.

⚠️ MEASUREMENT DIVERGENCE NOTE

These probability cones assume Freedom House historical dynamics (the AR(1) model is calibrated on FH data). The PTI-measured decline (−7.6/yr) falls outside the model’s 99th percentile (~3σ), reflecting a measurement divergence between indices rather than a model failure. Under Freedom House scoring (L=83), the US would begin near the democratic plateau, and the cone would project stable or improving governance with negligible probability of crossing instability thresholds.

Source: AR(1) Monte Carlo simulation (N=10,000, seed=42) using data-driven σ from 91-country Freedom House panel (1800–2025). Model: phase5-recalibrated-monte-carlo.py. Confidence intervals show p5/p25/p50/p75/p95 percentiles. Model calibrated on Freedom House data; PTI starting point.

Policy Implications & Normative Assessment

The following normative assessments are separated from the empirical analysis above. They reflect the author's interpretation of the data and should be evaluated independently from the statistical findings.

The recalibrated probability cone, using data-driven volatility and a Freedom House-calibrated AR(1) mean reversion model, projects a median trajectory from L=48 (PTI starting point) to L=65 by 2040 — a substantial improvement over the original thesis projection of L=8. The AR(1) model's mean reversion toward L*=80.9 is the dominant force, and even the worst-case (5th percentile) outcome remains above L=52. P(tyranny by 2040) is effectively zero under data-driven parameters. The original thesis claim of 62% is retracted. However, the starting position of L=48 remains contested: published indices place the US at L=65–83 (Freedom House: 83, V-Dem: 65–72). Under Freedom House scoring (L=83), the US begins near the equilibrium and projections would show the country firmly in the democratic plateau with minimal downside risk. The recalibration table in phase5-recalibrated-mc-results.md provides sensitivity analysis across starting values L=48 through L=84.