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

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 (α, σ, ε)—alignment, stake, and entropy—as candidate sufficient statistics for any resource-allocation configuration. We propose a friction functional, in its simplest candidate form F = σ(1 + ε)/(1 + α), whose comparative statics encode three structural predictions: friction increases in stakes, increases in entropy, and decreases in alignment. We are explicit that this form is a phenomenological ansatz, not a theorem; a companion study tests it in a multi-agent reinforcement-learning environment and finds the linear alignment dependence falsified by a U-shaped relationship, motivating a candidate quadratic form F = σ(1 + ε)/(1 + α²) presented as a refinement for future confirmation. 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, a measurement apparatus, and machine-checked Lean 4 proofs of the core comparative-statics. Illustrative applications to cryptocurrency governance and political legitimacy show the same architecture spanning domains—offered as candidate unification rather than established identity.