Regional Bias Explorer

Individual score (noisy)Structural level (set)Crowd mean (stable)
0255075100individuals in the sampled crowd →
Structural level of the region: 60
Per-person situational noise: ±30
Size of the sampled crowd: 40
The individual dots scatter by up to ±30 around the mean — a single person's score is a poor estimate of the region. Yet the crowd mean is 61.7, within 1.7 of the structural level 60, and the mean steadies as the crowd grows (mean absolute deviation 13.6). The aggregate, not the individual, carries the structural signal.

In the bias-of-crowds model an individual test score reads a fluctuating situational input, so it is noisy; the aggregate across many people cancels that noise and tracks the region's stable structural level. Raise the crowd size and watch the mean lock onto the structural line even as the individual dots stay scattered.

Structural Feedback Loop

Disparity over timeFixed point the loop settles to
0255075100successive periods →
Feedback strength of the structure: 80%
Initial disparity: 50
Fresh discriminatory input per period: 0
With feedback 80% and no fresh discriminatory input, disparity moves from 50 to 3.4 over 12 periods, settling toward a fixed point of 0.0. The loop sustains a moderate disparity that neither vanishes nor runs away.

Each period's disparity carries into the next through the structure — segregated capital, network-based hiring, under-resourced schools — so a strong enough loop sustains disparity with no new discrimination at all. Set fresh input to zero and raise the feedback: the disparity refuses to decay. That self-reproduction is what makes the racism systemic rather than a sum of present-day acts.

Cumulative Disparity Pipeline

Majority group (pass 0.60/gate)Minority group (pass 0.540/gate)
Number of sequential gates: 4
Per-gate relative gap: 10% (minority passes at 90% of the majority rate at every gate)
Gate
Majority
n
Minority
n
in
1000.0
1000.0
1
600.0
540.0
2
360.0
291.6
3
216.0
157.5
4
129.6
85.0
After 4 gates, 129.6 of the majority group and 85.0 of the minority group remain — an aggregate ratio of 0.6561, a 34.4% shortfall. The per-gate ratio 0.90 raised to the power 4 is 0.6561: the aggregate disparity is the per-gate gap compounded, even though no single gate differs by more than 10%.

A gap too small to notice or prove at any one gate becomes a large disparity across a chain of gates. This is cumulative disadvantage: the aggregate ratio equals the per-gate ratio raised to the number of gates, so adding gates multiplies the shortfall even when each gate is held fixed.