Behavioural Gradient Calculator

AoE: Architectures of Ease

Calculate compliance probability using the AoE formula: P(compliance) = σ[αF + βI + γC]. Explore how friction differentials, identity coupling, and future-cycle access combine to create enforcement-free compliance.

96.1%

Excellent Compliance

Probability of compliance without enforcement

AoE Mechanisms

F — Friction Differential0.60

Compliance is easier than defection

I — Identity Coupling0.50

How much compliance reinforces self-identity

C — Future-Cycle Access0.70

Value of maintaining future system access

CONTRIBUTION TO COMPLIANCE

37%

23%

39%

AoE FORMULA

P = σ[2.0×0.60 + 1.5×0.50 + 1.8×0.70]

P = σ[3.21] = 96.1%

Compliance Gradient (Sigmoid Function)

The sigmoid function maps the weighted sum of F, I, and C to compliance probability. Small changes near the threshold produce large behavioural shifts.

Hidden Costs: Enforcement vs Ease

Enforcement-based systems incur four hidden costs that ease-based design largely eliminates.

Sensitivity Analysis

How compliance changes when each mechanism varies by ±0.5 from current values.

Key Insights from AoE

Threshold Effects

Near the 50% threshold, small improvements in F, I, or C produce dramatic compliance shifts. This is the "S-curve" leverage point.

Mechanism Synergy

All three mechanisms (F, I, C) contribute independently. A system weak in one area can compensate with strength in others.

Self-Enforcing Design

When αF + βI + γC exceeds ~2.0, compliance exceeds 90% without any monitoring or enforcement infrastructure.

Read the AoE Paper View Explainer