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Delegation Risk

Risk Inheritance Calculator

Risk Inheritance Calculator

Section titled “Risk Inheritance Calculator”

Interactive tool for calculating how trust flows through delegation chains and networks.

How to Use

Section titled “How to Use”
  1. Add nodes representing principals, coordinators, and executors
  2. Add edges to define trust relationships between nodes
  3. Select a propagation rule
  4. Calculator shows effective trust from source to all reachable nodes

Nodes

Trust Edges

Propagation Rule

Effective trust = T₁ × T₂ × … × Tₙ along each path

Effective Trust from Source
TargetEffective TrustBest Path
Graph Visualization

Propagation Rules Explained

Section titled “Propagation Rules Explained”

Multiplicative (Default)

Section titled “Multiplicative (Default)”

The most common model. Trust compounds multiplicatively along a path:

Effective Trust = T₁ × T₂ × ... × Tₙ

Example: Principal trusts Coordinator at 0.9, Coordinator trusts Executor at 0.8

  • Effective trust: 0.9 × 0.8 = 0.72

Use when: Trust represents “probability of correct behavior” and failures are independent.

Minimum

Section titled “Minimum”

Trust is limited by the weakest link:

Effective Trust = min(T₁, T₂, ..., Tₙ)

Example: Same chain with 0.9 and 0.8

  • Effective trust: min(0.9, 0.8) = 0.8

Use when: Each link must independently meet a threshold (like security clearances).

Harmonic Mean

Section titled “Harmonic Mean”

Balanced approach that penalizes low values:

Effective Trust = n / (1/T₁ + 1/T₂ + ... + 1/Tₙ)

Example: Same chain with 0.9 and 0.8

  • Effective trust: 2 / (1/0.9 + 1/0.8) = 0.847

Use when: You want to balance between multiplicative (too pessimistic) and minimum (too optimistic).

Section titled “Weakest Link (Product of Complements)”

Models trust as “probability of not failing”:

Effective Trust = 1 - [(1-T₁) × (1-T₂) × ... × (1-Tₙ)]

Example: Same chain with 0.9 and 0.8

  • Failure probabilities: 0.1 and 0.2
  • Combined failure: 1 - (0.1 × 0.2) = 1 - 0.02 = 0.98

Use when: Failures must occur at multiple points simultaneously (redundant systems).

Multiple Paths

Section titled “Multiple Paths”

When multiple paths exist between source and target, this calculator shows the best path (highest effective trust). In practice, you might:

  1. Take the maximum (optimistic): If any path succeeds, trust is established
  2. Average paths (moderate): Blend multiple paths
  3. Use only verified paths (conservative): Only count audited delegation chains

Practical Examples

Section titled “Practical Examples”

Example 1: Simple Delegation Chain

Section titled “Example 1: Simple Delegation Chain”
Human → AI Orchestrator → Code Generator → Deployed Code


Trust levels: 0.95 → 0.80 → 0.70
Multiplicative: 0.95 × 0.80 × 0.70 = 0.532 (53.2%)

The effective trust to deployed code is only 53.2%, suggesting need for:

  • Additional verification at each step
  • Direct human review of deployed code

Example 2: Parallel Executors

Section titled “Example 2: Parallel Executors”
        ┌→ Executor A (0.9)
Human → Coordinator ─┤
        └→ Executor B (0.7)

With Coordinator trust at 0.85:

  • To Executor A: 0.85 × 0.9 = 0.765
  • To Executor B: 0.85 × 0.7 = 0.595

Executor B should have limited capabilities or additional oversight.

Example 3: Redundant Verification

Section titled “Example 3: Redundant Verification”
           ┌→ Verifier A (0.8) ─┐
Human → ──┤                     ├→ Action
           └→ Verifier B (0.8) ─┘

Using weakest link rule (both must pass):

  • If both verify independently: 1 - (0.2 × 0.2) = 0.96

Redundancy significantly increases effective trust.

Design Implications

Section titled “Design Implications”
Effective TrustImplication
> 80%Can operate with standard monitoring
60-80%Requires enhanced logging and periodic review
40-60%Needs active human oversight
< 40%Should not operate autonomously

Next Steps

Section titled “Next Steps”