New framework quantifies AI agent coordination friction with consent axiom

Murad Farzulla's new paper, "The Axiom of Consent: Friction Dynamics in Multi-Agent Coordination," presents a formal mathematical framework for understanding why multi-agent systems fail to coordinate effectively. The core insight: actions affecting agents require authorization in proportion to their stakes. From this single axiom, the paper derives a friction functional F = σ(1+ε)/(1+α), where σ is stake, ε is entropy (information uncertainty), and α is alignment (shared interests). Higher stakes or entropy increase friction; better alignment reduces it. The framework includes machine-checked Lean 4 proofs for comparative statics, a measurement apparatus, and applications to real-world domains like crypto governance and political legitimacy.

Practically, the model reframes consent-based coordination as a natural dynamical attractor: lower-friction configurations persist longer under selection pressure from the Replicator-Optimization Mechanism. This means systems that respect stakeholder consent are not just normatively preferable but evolutionarily stable. The paper provides a rigorous tool for designing resilient multi-agent systems—whether in AI agent swarms, DAO governance, or democratic institutions. With 94 pages of formal development and empirical companion references, it bridges theoretical computer science and social coordination, offering a new lens for debugging coordination failures in increasingly autonomous multi-agent environments.