The Axiom of Consent: Friction Dynamics in Multi-Agent Coordination

Abstract

Multi-agent systems face a fundamental coordination problem: agents must coordinate despite heterogeneous preferences, asymmetric stakes, and imperfect information. When coordination fails, friction emerges—measurable resistance manifesting as deadlock, thrashing, communication overhead, or outright conflict. This paper derives a formal framework for analyzing coordination friction from a single axiom: actions affecting agents require authorization from those agents in proportion to stakes. From this axiom of consent, we establish the kernel triple (alpha, sigma, epsilon)—alignment, stake, and entropy—as candidate sufficient statistics for any resource-allocation configuration. We propose a friction functional whose comparative statics encode three structural predictions: friction increases in stakes, increases in entropy, and decreases in alignment. The Replicator-Optimization Mechanism governs evolutionary selection over coordination strategies: configurations generating less friction persist longer, establishing consent-respecting arrangements as dynamical attractors rather than normative ideals. We develop formal definitions for resource consent, coordination legitimacy, and friction-aware allocation, plus machine-checked Lean 4 proofs of the core comparative-statics. Illustrative applications to cryptocurrency governance and political legitimacy show the same architecture spanning domains. v3.0.0 (2026-07-11): Matches arXiv v3 (94pp). The MARL empirical appendix has been split out into a standalone companion paper; total-variation legitimacy remark added (proved), reconciling the level-form dynamics with the total-variation measurement form; α-domain fixes; hedging pass throughout.