Theoretical Foundations

Theoretical Foundations

Theoretical Content

These documents explore the mathematical and economic foundations of delegation risk. They provide formal frameworks that underpin the practical applications in other sections.

Note on terminology: These pages use “risk” (as in Delegation Risk) and “trust” somewhat interchangeably. Higher trust in a delegate means lower risk from that delegation. The framework is fundamentally about managing risk, but trust is a useful complementary concept.

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Documents

Core Framework Theory

For the foundational concepts (Agency, Power, Authority, Strong Tools), see the Framework section which contains the core theoretical contributions alongside the risk formalization.

Risk Mechanics

• Risk Dynamics — Bayesian updating, how risk estimates evolve over time
• Risk Accounting — Risk ledgers, balance sheets, auditing
• Delegation Economics — Production functions, depreciation models

Delegation at Scale

• Human-AI Delegation — Calibration, handoffs, hybrid systems
• Risk at Scale — Statistical properties, organizational challenges
• Delegation Interfaces — Boundaries, APIs, contracts

Risk Systems

• Risk Optimization — Portfolio allocation, efficiency frontiers
• Delegation Protocols — Handshakes, verification, revocation
• Risk Inheritance — Delegation chains, transitivity

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Relationship to Practice

These theoretical foundations inform:

• Protocol multipliers in the Protocol Catalog
• Track record calculations in the Insurance Bot
• Exposure modeling in Delegation Accounting