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

TL;DR

This paper introduces a formal framework for understanding coordination friction in multi-agent systems based on an axiom of consent, predicting how preference alignment, stakes, and communication entropy influence coordination difficulty.

Contribution

It develops a novel axiomatic approach and a predictive friction equation for multi-agent coordination, linking resource allocation, consent, and friction dynamics across domains.

Findings

Higher preference alignment leads to faster convergence in MARL systems.

Accounting for stake asymmetry reduces coordination failures.

Interpretability gaps in AI increase friction proportional to human-AI alignment issues.

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) characterizing any resource allocation configuration. The friction equation $F = {\sigma} (1 + {\epsilon})/(1 + {\alpha})$ predicts coordination difficulty as a function of preference alignment ${\alpha}$, stake magnitude ${\sigma}$, and communication entropy ${\epsilon}$. The Replicator-Optimization Mechanism (ROM) 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 in multi-agent systems. The framework yields testable predictions: MARL systems with higher reward alignment exhibit faster convergence; distributed allocations accounting for stake asymmetry generate lower coordination failure; AI systems with interpretability deficits produce friction proportional to the human-AI alignment gap. Applications to cryptocurrency governance and political systems demonstrate that the same equations govern friction dynamics across domains, providing a complexity science perspective on coordination under preference heterogeneity.