Scalability of Morality: A Particle-Based Numerical Study on the Decoupling of Law and Ethics in Large-Scale Populations

Abstract

This study introduces a particle-based computational framework to investigate the scalability of morality and the systemic decoupling of formal law from decentralized social ethics in expanding populations. While micro-societies reinforce ethical conduct through local reciprocity, macroscale systems introduce anonymity that strains cognitive memory limitations. We model individual agents as discrete particles with finite memory capacities ($L$) and dynamically evolving, stochastic choice profiles ($μ$) regulated by non-linear social pressure switches. Monte Carlo ensemble simulations demonstrate a distinct, non-linear phase transition as the population scales ($N \to \infty$). When the population metric outpaces memory capacity ($N \gg L$), the local re-encounter probability drops as $\mathcal{O}(L/N)$. This structural dilution neutralizes decentralized peer-to-peer accountability, causing global behavioral norms to decouple from moral baselines and drift toward a minimalist legal floor. Furthermore, cyclic scale experiments expose a prominent, path-dependent hysteresis loop, mathematically formalizing the non-Markovian inertia and irreversible nature of moral decay in self-organizing social systems.