Haghrah & Haghrah model shows large populations decouple ethics from law

Amir Arslan Haghrah and Amir Aslan Haghrah have published a paper on arXiv introducing a particle-based computational framework to study the scalability of morality. Their model treats individual agents as particles with finite memory capacity ($L$) and stochastic choice profiles ($\mu$) regulated by non-linear social pressure switches. Monte Carlo ensemble simulations reveal a sharp, non-linear phase transition: when the population size $N$ far exceeds $L$, the local re-encounter probability decays as $\mathcal{O}(L/N)$, effectively neutralizing decentralized peer-to-peer accountability.

This structural dilution causes global behavioral norms to decouple from ethical baselines and drift toward a minimalist legal floor. The authors also identify a hysteresis loop in cyclic scale experiments, mathematically formalizing the irreversible inertia of moral decay. The work bridges multiagent systems and control theory, offering a quantitative lens on why large societies often rely on formal legal systems rather than emergent ethics. It also raises questions for AI safety: multi-agent systems with finite memory may similarly suffer from ethical drift as they scale.