An axiomatic theory ties coordination breakdowns to misalignment, high stakes and uncertainty, proposing a simple friction metric that rises with stakes and entropy and falls with alignment; the results are machine-verified but remain empirically untested.

Main Finding

The paper axiomatizes coordination friction in multi-agent systems from a single “axiom of consent”: actions that affect agents require authorization from those agents in proportion to their stakes. From this axiom it derives a small kernel of primitives—alignment (α), stakes (σ), and entropy/information loss (ε)—and proposes a simple phenomenological friction functional F = σ · (1+ε) / (1+α) whose comparative statics generate three structural predictions: friction rises with stakes σ, rises with information loss ε, and falls with alignment α. Evolutionary selection over coordination configurations is modeled by the Replicator-Optimization Mechanism (ROM): low-friction, high-legitimacy configurations persist as dynamical attractors. The framework is formalized (including machine-checked Lean 4 proofs), operationalized with measurement protocols, and illustrated in domains from cryptocurrency governance to political legitimacy and AI alignment.

Key Points

• Axiom of consent: authority over actions affecting agents should be proportional to the agents’ stakes; deviations generate measurable friction.
• Kernel triple (α, σ, ε):
  • Alignment α: correlation between decision-makers’ preferences and affected parties’ preferences.
  • Stakes σ: magnitude of consequences borne by affected parties.
  • Entropy ε: information loss / uncertainty in transmission between decision-makers and affected parties.
• Friction functional (phenomenological ansatz): F = σ (1+ε)/(1+α). Characteristic implications:
  • ∂F/∂σ > 0 (higher stakes → more friction),
  • ∂F/∂ε > 0 (more information loss → more friction),
  • ∂F/∂α < 0 across cooperative range (more alignment → less friction). The author is explicit that this specific algebraic form is an ansatz satisfying desiderata, not a proved law; alternative forms were considered and some refinements rejected after companion empirical work.
• ROM dynamics: generalized replicator–mutator equations weight configuration persistence by stakes and penalize by friction; legitimacy and friction shape evolutionary selection of governance/coordination arrangements.
• Formal foundations: convergent derivations from constrained optimization, information decomposition and diversity decomposition are provided; core comparative-statics are machine-checked in Lean 4.
• Empirical & operational apparatus: proposals for measuring α, σ, ε (survey/revealed preference, transfer entropy, economic/political/computational proxies), friction proxies (market volatility, institutional instability, coordination-failure metrics), and identification strategies (IV, RDD, DiD, synthetic controls).
• Companion empirical work (Farzulla, 2026a) tested the friction form in multi-agent RL: after correcting preference-sign design, alignment effects were signed and monotone (cooperative alignment lowers friction; opposition shows no advantage over indifference), prompting withdrawal of a symmetric quadratic refinement and supporting a 1/(1+α) denominator over the cooperative range.
• Pathologies & caveats: coercion/authoritarian suppression can mask friction, low observed friction does not necessarily imply normative legitimacy, measurement error and domain-specific calibration issues remain important.

Data & Methods

• Theoretical methods:
  • Axiomatic derivation from the axiom of consent.
  • Convergent derivations using constrained optimization, information-theoretic decomposition, and diversity decomposition to justify the kernel triple.
  • Phenomenological construction of the friction functional under stated desiderata (appendix formal characterizations and discussion of under-determination).
  • Dynamical model: ROM (replicator–optimization / replicator–mutator family) giving update equations for configuration frequencies with explicit weighting by stakes, legitimacy, friction, and mutation/entropy.
  • Formal verification: key comparative-statics and properties proved in Lean 4.
• Empirical / operational methods:
  • Measurement protocols for α (surveys, revealed preference, transfer-entropy/time-series causality), σ (economic/political/computational stakes metrics), ε (information-theoretic measures, bandwidth proxies).
  • Friction proxies: market volatility, institutional instability indices, direct coordination-failure counts.
  • Identification strategies: instrumental variables, regression discontinuity, difference-in-differences, synthetic controls.
• Empirical status: the friction functional is explicitly labeled a testable ansatz. Companion multi-agent RL experiments provided partial validation (signed monotone alignment effect) and led to rejecting some symmetric refinements. Full cross-domain empirical validation remains future work.

Implications for AI Economics

• Governance & market design:
  • Aligning decision authority (voice/consent) with consequence-bearing stakes reduces coordination friction—designs for AI governance, standards, and markets should prioritize voice mechanisms proportional to impacted stakes.
  • Concentration of stakes (large σ) raises friction; redistribution or delegation architecture that diffuses stakes can lower coordination resistance.
• Information policy:
  • Reducing entropy (ε) via transparency, auditing, improved observability and communication channels between decision-makers and affected agents will reduce friction; transfer-entropy–based monitoring is recommended for dynamic alignment measurement.
• Mechanism design:
  • Mechanism designers should treat friction as an observable cost; mechanisms that minimize friction (not just maximize static welfare) will be evolutionarily favored in decentralized settings.
  • Design objectives should target the fitness landscape (legitimacy and friction) because ROM dynamics imply that low-friction institutional arrangements persist even absent explicit normative choice.
• AI deployment & coordination risks:
  • AGI or transformative AI can act as an evolutionary shock altering alignment/authority structures; anticipating how shocks reweight stakes and alignment is crucial for institutional resilience.
  • Coercive suppression of friction can produce apparent short-term stability but may mask systemic risks—regulatory evaluation must account for latent friction.
• Research & policy agenda:
  • Need for empirical validation across economic settings (markets, compute allocation, platform governance) and computational implementation in multi-agent RL/market simulations.
  • Practical levers: (1) increase alignment between operators and affected agents; (2) reduce information asymmetries; (3) redistribute or account for stakes in decision protocols.
• Cautions:
  • The proposed friction form is underdetermined; domain-specific calibration and causal identification are required before direct policy prescriptions.
  • Measurement challenges (proxy validity, confounding, scale-mixing) make careful empirical protocols essential for translating the framework into economic policy.