Variational Mechanics of Moral Hysteresis: A McKean–Vlasov Framework for Normative Collapse and Recovery

We propose a mean-field model in which the collapse and recovery of social norms appear as hysteretic transitions in a population of interacting agents. Each agent carries a continuous moral state xₜ ∈ ℝ, interpreted as a coarse-grained propensity to choose norm-compliant rather than norm-violating actions in a given context. The dynamics follow an interacting diffusion dxₜ = −∂ₓV(xₜ, mₜ; λ) dt + √(2D) dWₜ, where V(x, m; λ) is an effective potential, mₜ is the population mean moral state, λ is a control parameter (e.g. antisocial reward or perceived corruption level), D is a noise amplitude, and Wₜ is a Wiener process. Social influence enters via a mean-field coupling of strength κ and a prosocial field h. In the large-population limit, the empirical distribution of moral states converges to a solution of a nonlinear Fokker–Planck (McKean–Vlasov) equation. For a double-well potential with mean-field coupling, the stationary solutions exhibit monostable and bistable regimes as (λ, κ, D, h) vary. Under quasi-static driving of λ from low to high values and back, starting from high- and low-norm initial conditions, the system traces a hysteresis loop in the (λ, m*) plane, where m*(λ) is the quasi-stationary mean at fixed λ. We define collapse and recovery thresholds λ_coll and λ_rec, the hysteresis width Δλ = λ_coll − λ_rec, and the loop area A_hyst and estimate them numerically from finite-population simulations. We then introduce a McKean–Vlasov free-energy functional to interpret these phenomena in variational terms, distinguishing binodal lines (thermodynamic coexistence of high- and low-norm phases) from spinodal lines (loss of dynamical stability of a given phase), and we sketch Kramers-type estimates for escape times between basins. In the parameter regimes explored, stronger social coupling widens the hysteresis loop, intermediate noise facilitates recovery from low-norm regimes, and variance, autocorrelation and recovery time of the mean moral state increase near λ_coll, consistent with critical slowing down. We conclude by discussing how this formalism could be connected, at least qualitatively, to behavioural experiments and survey indicators of norm stability and change.