Appendix: Cluster Analysis

A data-driven exploration of the natural groupings, the safety divide, and hardware vs. software beliefs among 1,793 ESPAI 2024 cleaned analysis rows.

Executive Summary

1. How Many Camps? The Natural Clusters

1.1 Clustering on Value Outlook (n=1,538)

The value-of-HLMI question asked respondents to assign probabilities (summing to 100%) across five outcomes: extremely good, on balance good, neutral, on balance bad, and extremely bad. It is the highest-coverage feature in this analysis. We cluster on these 5 dimensions using Gaussian Mixture Models.

Figure 1: Silhouette scores for K=2 through K=6 clusters on value outlook. K=2 has the highest silhouette, but K=3 and K=4 offer more interpretable structure.

Silhouette scores are modest (0.10-0.12), indicating the clusters are not sharply separated -- this is a continuous landscape of opinion, not discrete tribes. Still, the structure is meaningful.

1.2 Four-Camp Solution

Figure 2: Four natural camps in value outlook. Left: PCA projection. Center: mean probability profiles. Right: cluster sizes.

The most striking finding here is the Polarized/Bimodal group. These respondents assign high probability to both extremely good and extremely bad outcomes -- their P(extremely good) is comparable to the Strong Optimists, yet they simultaneously assign substantial probability to catastrophic outcomes. This is not a group of doomers or technophobes. They are researchers who believe AI will be hugely impactful, but who are genuinely torn on whether that impact will be positive or negative. The key axis for this group is magnitude of impact, not direction -- they have rejected the possibility that AI will be a modest or neutral development.

1.3 Three-Camp Solution (Simpler View)

Collapsing to 3 clusters (which has a higher silhouette score of 0.18 vs 0.07) merges the finer distinctions into a simpler optimist/moderate/pessimist framing. This loses the polarized group but provides a cleaner summary:

Figure 3: Three-camp simplification. The polarized group is absorbed into the moderate/pessimist clusters.

1.4 Intuitive View: How Soon vs. How Good

The PCA axes above lack intuitive meaning. Below, we plot each respondent on two directly interpretable dimensions: their predicted HLMI arrival year (x-axis) and their net optimism score (y-axis), defined as P(good + extremely good) minus P(bad + extremely bad). This reveals where the four camps sit in the space of "how soon" vs. "how beneficial."

Figure 3b: Respondents (n=935) binned by predicted HLMI year and net optimism. Each bubble's size shows how many researchers from that cluster fall in the bin (labeled when ≥5). The vertical dashed line marks the median predicted year; the horizontal line separates net optimists from net pessimists.

1.5 Combined Clustering: Values + Concerns + Safety + Extinction

For the 191 respondents who answered all of: value outlook, concern scenarios, alignment-problem importance, and extinction/disempowerment probability, we ran a richer clustering incorporating 8 features.

Figure 4: Combined clustering incorporating worldview, concerns, safety/alignment-problem views, and extinction/disempowerment probability. Mean concern averages 11 scenario concern ratings on a 0-3 scale (0=no concern, 3=extreme concern); alignment-problem importance is a 0-4 ordinal score (0=not a real problem, 4=among the most important problems in the field); P(extinction/disempowerment) is a percentage.

HLMI year summaries include the median, interquartile range, mean, and item-level n because several groups share the same median year while their wider distributions differ.

2. Higher vs Lower Safety/Severe-Risk Concern

2.1 Defining the Groups

We built a safety composite score from (normalized 0-1 and averaged):

• Alignment-problem importance rating (0-4 ordinal scale: not a real problem to among the most important problems in the field)
• Value of working on the alignment problem today compared with other AI problems (0-4 ordinal scale)
• P(extinction/disempowerment from AI) (0-100%)

Requiring at least 2 of 3 components, we obtained scores for 754 respondents and split at the median (0.500) into High (n=330) and Low (n=424) safety concern groups.

2.2 The Full Comparison

Figure 5: Comprehensive comparison of higher vs lower safety/severe-risk-concern respondents across six dimensions. Alignment-problem importance uses the 0-4 ordinal scale above; mean concern averages 11 scenario concern ratings on a 0-3 scale; the optimism-maximizing AI progress-rate answer is coded 0=much slower, 2=current speed, 4=much faster.

2.3 Statistical Tests

Selected Mann-Whitney U tests for scalar summaries from Figure 5. The value-outlook panel is summarized by P(extremely good) and P(extremely bad), the concern panel by mean concern, and the AI-capabilities panel is tested item-by-item in the next table. Effect size r is rank-biserial correlation (|r| > 0.3 = medium, |r| > 0.5 = large). Scale notes: mean concern 0-3, optimism-maximizing AI progress-rate answer 0-4, probabilities in percentage points. *** p<0.001, ** p<0.01, * p<0.05

2.4 AI Capabilities by 2044: What Do Safety People Expect?

Safety-concerned people don't just worry more -- they have systematically different expectations for what AI will be able to do by 2044:

Scale: 0=Very unlikely, 1=Unlikely, 2=Even chance, 3=Likely, 4=Very likely. High - Low is the high-safety mean minus the low-safety mean, so positive values mean high-safety respondents rated the capability as more likely. Hypothesized direction is marked for risk-relevant capabilities where we expected High > Low; other rows are exploratory.

2.5 Intelligence Explosion Beliefs

Figure 6: Probability estimates for intelligence explosion scenarios, by safety concern level.

3. Hardware vs. Software Progress Beliefs

3.1 Counterfactual Progress Reduction if Factors Were Halved

Respondents rated how much AI progress would decrease if each of 5 factors were cut in half (0-100% scale). Higher values mean the factor is more important.

Figure 7: Counterfactual progress-factor analysis. Top-left: estimated progress reduction distributions. Top-right: hardware vs algorithm progress-reduction estimates. Bottom-left: HW-SW index distribution. Bottom-right: factor correlations with other variables.

3.2 Hardware vs Software Index

We computed (Hardware - Algorithms) / (Hardware + Algorithms) for each respondent who rated both. Positive = hardware-leaning, negative = software-leaning.

3.3 Do Progress Beliefs Predict Other Views?

Significant cause-factor correlations (p < 0.10)

Hardware-Software Index Correlations

3.4 Progress Beliefs by Outlook and Safety Groups

Do optimists, pessimists, and safety-concerned researchers differ in what they think drives AI progress? Below we break down cause factor importance by outlook cluster (left) and safety group (right).

Figure 7b: Mean importance ratings for each progress factor, split by outlook group (left) and safety group (right). Scale: 0-100% estimated decrease in progress if factor halved.

4. How Outlook Predicts Everything Else

The three value-outlook clusters (from Section 1) predict views across many other dimensions:

Values are medians with sample sizes in parentheses, except HLMI Year, which shows median [IQR], mean, and item-level n because several groups share the same median year. Scale notes: alignment-problem importance 0-4, mean concern 0-3, optimism-maximizing AI progress-rate answer 0=much slower to 4=much faster, probabilities in percentage points.

Figure 8: How the four value-outlook camps compare across timelines, extinction/disempowerment probability, safety/alignment-problem views, concern levels, optimism-maximizing AI progress-rate answers, and P(extremely bad). Mean concern averages 11 scenario concern ratings on a 0-3 scale; alignment-problem importance and optimism-maximizing AI progress-rate answers use 0-4 ordinal scales.

5. What Dimensions Structure AI Researcher Beliefs?

Principal Component Analysis on respondents with values + concerns + safety + extinction/disempowerment data (n=180) reveals the latent axes of disagreement.

Figure 9: PCA factor loadings. Green bars = positive loading, red = negative. Each panel shows one principal component.

6. The Full Correlation Structure

Figure 10: Spearman rank correlations between key variables. Stars indicate significance. Sample sizes shown in each cell. Alignment-problem importance uses a 0-4 ordinal scale from not a real problem to among the field's most important problems; value of working on the alignment problem today uses a 0-4 ordinal scale from much less valuable to much more valuable than other AI problems; mean concern uses a 0-3 scale; HLMI Year is a calendar-year estimate; probabilities are 0-100 percentages.

Key Pairwise Correlations

7. Methods & Caveats

7.1 Approach

• Strategy: Multiple focused analyses on overlapping subsets (rather than one clustering requiring all features, which drops to n~180). This maximizes statistical power while giving complementary views.
• Clustering: Gaussian Mixture Models (GMM) with full covariance, 10-20 random initializations, model selection by BIC with parsimony preference
• Statistical tests: Non-parametric throughout (Mann-Whitney U for two groups, Kruskal-Wallis for three+, Spearman rank correlations)
• Visualization: PCA for dimensionality reduction (visualization only -- clustering done in full feature space)

7.2 Caveats

7.3 Technical Details

• Random seed: 42
• All tests two-sided; no multiple comparison correction (exploratory analysis)
• HLMI year capped at 2150 for visualization; uncapped for statistics where noted