Correlation Can Be Good:
What Matters Is the Process

Overview

This project brings together two complementary lines of research. The first (Pilgrim & Becker, arXiv) shows that social communication reliably improves individual accuracy even when group accuracy gets worse — and derives a mathematical decomposition that explains why. The second (CI Abstract 2024) shows that even a perfectly accurate crowd can make the wrong decision by vote, because the crowd average and the plurality vote can be statistically "decoupled."

Paper 1 — Individual vs Crowd Accuracy After Social Influence

Citation: Pilgrim & Becker (2024). "Communication Reliably Improves Individual But Not Group Accuracy." arXiv:2407.00199.

Core Decomposition

After social influence, the change in mean squared error decomposes as:

Key Components

• Calibration: correlation between influence weight and initial accuracy (positive = good for crowd).
• Herding: correlation between influence weight and being close to the mean (can be negative for crowd).
• Centralization: how concentrated influence is in the network.

Empirical Findings (6 datasets)

Table shows proportion of group-question trials where accuracy improved after social influence. Results are computed live from the R pipeline output.

Figures

Figure generated by R pipeline

Figure 1. Proportion of trials where accuracy improved after social influence, comparing individual vs crowd level across datasets.

Figure generated by R pipeline

Figure 2. Scatter of ΔCrowd MAE vs ΔIndividual MAE. Most points fall in the lower half (individual improves) regardless of crowd direction.

Figure generated by R pipeline

Figure 3. Variance reduction after social influence across datasets. Variance almost always decreases — this mechanically produces individual improvement.

Empirical Analysis — Crowd vs. Individual Accuracy

Direct empirical comparison of crowd accuracy (group average) versus individual accuracy across 3 datasets with known true values (Gurcay et al. 2015, Navajas et al. 2018, Jayles et al. 2021), using mean absolute error (MAE) on round-1 estimates. Improvement ratio = individual MAE / crowd MAE; values above 1 indicate the crowd outperforms the average individual. Pooled geometric mean ratio = 2.06 (95% bootstrap CI: 1.77–2.43) across 178 questions — the crowd consistently beats the average individual by roughly a factor of two. (Kao 2018 and Mercier et al. 2022 are in the combined dataset but lack ground-truth values and are therefore excluded from this accuracy comparison.)

Figure generated by R pipeline

Figure 4. Meta-analysis: distribution of crowd improvement ratios pooled across all datasets. Ratio > 1 = crowd beats average individual. Vertical line at 1.0; shaded region shows 95% CI.

Figure generated by R pipeline

Figure 5. Crowd improvement ratio by dataset. Each row shows mean + 95% CI for one study. Overall pooled estimate shown at bottom.

Paper 2 — Estimates Are Not Decisions

Citation: Pilgrim & Becker (2024). "Estimates are Not Decisions: How Wise Crowds Can Make Unwise Choices." Collective Intelligence 2024.

Core Finding: Vote–Average Decoupling

The Model

N people estimate M options. Option k has mean μ_k = k × S, standard deviation σ = 1. Each person votes for their highest estimate.

Illustrative Example (3 Voters, 2 Options)

Average correctly identifies Option 2 as best (67 > 50), but the vote goes 2–1 for Option 1.

Datasets

Implications

The two papers together suggest that (1) social influence is not inherently harmful to collective intelligence — it can reliably improve individual accuracy — but (2) the aggregation method used to convert beliefs into decisions critically matters. Averaging dominates voting across a wide range of empirically realistic parameters.