Abstract
<title>Abstract</title> <p>This is the empirical companion to the Axiom of Consent, which derives a consent-friction functional F = σ(1+ε)/(1+α) from a single axiom and leaves its adequacy open. We test that functional in a four-agent shared-resource MARL environment—a 5×5×5 factorial of 125 conditions, 30 independent replications each—3,750 Independent Q-Learning (IQL) training runs, with an additive value-decomposition learner (VDN) re-run alongside on reduced control grids—and report two things: an honest characterization of which of its variables survive, and a methodological control battery showing how design choices manufacture spurious coordination findings. The kernel variables matter directionally, but the specific monotone form is rejected as a single-index predictor on comparative grounds (an independent-effects model decisively beats it; on the signed re-test the form itself clears the pre-registered absolute fit bar for VDN). The control battery then peels back three artifacts: the dominance of stakes is mechanical (reward is degree-1 homogeneous in σ; the ranking inverts under stake-normalization, though the direction—higher stakes raise friction—holds); the symmetric U-shape of the initial factorial is a sign-blind data-generating-process artifact (a shared-anchor sampler realizes correlation α²/(α²+(1−|α|)²), never negative); and opposition-helps never materializes in any tested design—at a genuine, sign-verified ρ = −1 (n = 2, no PSD cap) opposition shows no detectable advantage over indifference and at most fragilely loses to it, never beats it. The one surviving structural effect—cooperative alignment lowers the coordination gap (only the VDN cooperation-beats-indifference contrast survives Holm correction, Holm-adjusted p = 0.0072; the IQL direction corroborates; η² ≈ 0.036–0.058)—is shared-state-contention-mediated: it flattens entirely when each agent is given its own separable resource pool (ρ-slope → 0, n.s.), and a parametric partial-sharing sweep grades it as a monotone dose–response in contention degree (per-overlap ρ-slopes null at low sharing and significant only once a majority of resources are shared; the single continuous ρ×overlap interaction is significant (p ≈ 0.002–0.003) but a misspecified summary—the categorical per-overlap model C(w)×ρ is AIC-preferred (nested F, p ≤ 0.004, both learners)—so the per-overlap slopes, not the pooled linear term, carry the dose–response; a perfect but low-power Spearman = −1.000 over four overlap levels), bounding the claim to common-pool environments. A feasibility–learning decomposition downgrades even this survivor: the decline is the achievable joint optimum rising toward cooperation (feasibility), not reduced learning friction—once feasibility is controlled the learning shortfall does not fall. We give the formal desiderata, the competing functional forms, Holm-adjusted contrasts, and the verification each control implements, so the test stands alone and feeds back to the formal paper which variables to keep.</p>