Chapter 15: Probability Distributions
The Shape of Uncertainty
Probability distributions reveal not just what’s likely, but the full range of possibilities and their relative chances. This chapter visualizes and interprets the probability landscape emerging from our 1.3 billion simulations.
Understanding the Distributions
What Probability Distributions Tell Us
Beyond simple percentages, distributions reveal:
- Central tendency: Most likely outcomes
- Spread: Range of uncertainty
- Skewness: Asymmetric risks
- Tails: Extreme possibilities
- Modality: Single vs multiple peaks
Each distribution tells a story about the future’s shape.
Hypothesis Probability Distributions
H1: AI Progress Trajectory
Distribution Characteristics:
- Type: Strongly right-skewed
- Mean: 91.1%
- Median: 93.2%
- Standard Deviation: 5.7%
- 95% CI: [75.1%, 98.1%]
Interpretation: The distribution shows overwhelming probability mass toward continued progress. The long left tail represents low-probability barriers, but the peak is sharp and decisive. This is as close to certainty as forecasting allows.
H2: AGI Achievement
Distribution Characteristics:
- Type: Nearly uniform
- Mean: 44.3%
- Median: 44.1%
- Standard Deviation: 16.9%
- 95% CI: [14.6%, 80.1%]
Interpretation: This remarkably flat distribution represents true uncertainty. Evidence is so balanced that probability mass spreads almost evenly across the range. We genuinely don’t know.
H3: Employment Impact
Distribution Characteristics:
- Type: Left-skewed (toward displacement)
- Mean: 74.9% displacement
- Median: 77.3%
- Standard Deviation: 9.9%
- 95% CI: [54.9%, 90.8%]
Interpretation: The distribution leans heavily toward job displacement with a sharp peak around 75-80%. The tail toward complementarity exists but carries little probability mass.
H4: Safety Outcomes
Distribution Characteristics:
- Type: Bimodal
- Primary Peak: 62% (safe)
- Secondary Peak: 35% (risky)
- Standard Deviation: 13.3%
- 95% CI: [36.6%, 86.3%]
Interpretation: Unusual bimodal structure suggests two distinct equilibria. Either we achieve safety through coordination or fail dramatically—middle ground is unstable.
H5: Development Model
Distribution Characteristics:
- Type: Strongly left-skewed (toward centralization)
- Mean: 77.9% centralized
- Median: 81.2%
- Standard Deviation: 12.7%
- 95% CI: [48.9%, 95.8%]
Interpretation: Economic forces create strong pull toward centralization. The distribution’s shape suggests this is nearly inevitable without intervention.
H6: Governance Evolution
Distribution Characteristics:
- Type: Left-skewed (toward authoritarianism)
- Mean: 63.9% authoritarian
- Median: 66.4%
- Standard Deviation: 13.3%
- 95% CI: [39.0%, 87.8%]
Interpretation: Democracy faces headwinds. The distribution’s leftward lean shows authoritarian drift as the path of least resistance.
Scenario Probability Distributions
Top Scenarios Show Sharp Peaks
ABBABB (Rank 1: 11.59%):
- Sharp peak, narrow distribution
- Standard deviation: 1.2%
- Robust across models
- High confidence prediction
AABABB (Rank 2: 9.21%):
- Clear peak, moderate spread
- Standard deviation: 1.8%
- Some model sensitivity
- Good confidence
Mid-Tier Scenarios Show Broader Distributions
Scenarios ranking 20-40 show:
- Wider distributions
- Multiple smaller peaks
- Higher uncertainty
- Model dependence
Low Probability Scenarios Are Flat
Bottom tier scenarios show:
- Nearly uniform distributions
- No clear peaks
- High uncertainty
- Extreme model sensitivity
Temporal Evolution of Distributions
Uncertainty Funnel
Plotting distributions over time reveals a funnel pattern:
2025: Wide Distributions
- High uncertainty
- Multiple peaks
- Overlapping scenarios
- Intervention possible
2030: Separating Peaks
- Distributions sharpen
- Peaks diverge
- Overlap decreases
- Paths crystallizing
2035: Distinct Distributions
- Sharp peaks
- Clear separation
- Little overlap
- Paths locked
2040-2050: Narrow Peaks
- Very sharp distributions
- No overlap
- Fixed outcomes
- Change difficult
Joint Probability Distributions
Correlation Structures
Examining joint distributions reveals dependencies:
H1-H2 Joint Distribution:
- Strong positive correlation
- Progress drives AGI probability
- Conditional probability shifts
H5-H6 Joint Distribution:
- Very strong correlation
- Centralization enables authoritarianism
- Near-linear relationship
H3-H6 Joint Distribution:
- Moderate negative correlation
- Displacement threatens democracy
- Threshold effects visible
Distribution Clustering
Three Meta-Distributions Emerge
When we overlay all 64 scenario distributions, three distinct clusters appear:
Cluster 1: Adaptive Integration
- Center: 42% probability
- Spread: ±8%
- Shape: Normal-like
- Stability: High
Cluster 2: Fragmented Disruption
- Center: 31% probability
- Spread: ±11%
- Shape: Left-skewed
- Stability: Medium
Cluster 3: Constrained Evolution
- Center: 27% probability
- Spread: ±10%
- Shape: Right-skewed
- Stability: Medium
Extreme Value Analysis
Tail Risks
Right Tail (Best Cases):
- Probability of utopian outcomes: <0.1%
- Maximum achievable success: ~85% positive across all dimensions
- Requires perfect coordination
Left Tail (Worst Cases):
- Probability of dystopian collapse: 2.3%
- Maximum failure: ~95% negative across all dimensions
- Results from cascade failures
Black Swan Potential
Fat tails in several distributions suggest:
- Extreme events more likely than normal distribution predicts
- Cascade effects can amplify
- Prepare for 1-in-100 events
Sensitivity of Distributions
To Evidence Quality
Higher quality evidence → Sharper distributions Lower quality evidence → Flatter distributions
To Causal Model
Conservative model → More uniform distributions Aggressive model → More extreme peaks
To Time Horizon
Near term → Broader distributions Long term → Sharper peaks (path dependency)
Confidence Calibration
How Sure Are We?
Comparing predicted distributions to confidence levels:
Overconfident on:
- None identified
Well-calibrated on:
- AI progress
- Employment impact
- Centralization
Underconfident on:
- AGI timing
- Governance outcomes
Key Distribution Insights
1. Certainty Is Rare
Only H1 (AI progress) shows overwhelming directional certainty. Everything else has meaningful uncertainty.
2. Bimodality Is Common
Several distributions show multiple peaks, suggesting discrete equilibria rather than continuous outcomes.
3. Skewness Reveals Bias
Most distributions lean toward negative outcomes, suggesting positive futures require active effort.
4. Tails Matter
Fat tails mean extreme scenarios, while unlikely individually, collectively represent significant probability.
5. Time Sharpens
Distributions narrow over time as path dependencies lock in, making early intervention critical.
Using Distributions for Decision-Making
For Risk Management
- Focus on full distribution, not just means
- Prepare for tail events
- Understand skewness direction
For Strategic Planning
- Plan for distribution peaks
- Prepare for full range
- Monitor distribution shifts
For Investment
- Diversify across distribution
- Hedge tail risks
- Position for multiple peaks
The Distributions’ Message
The probability distributions tell us:
- Few things are certain (except AI progress)
- Multiple equilibria exist (bimodal distributions)
- Negative outcomes are “downhill” (skewness)
- Time reduces options (narrowing distributions)
- Extremes are possible (fat tails)
Understanding these distributions means understanding not just what’s likely, but the full landscape of possibility—and that’s essential for navigating uncertainty.