Wealth Stratification, Norm Contagion, and Institutional Capture: An Agent-Based Model of Endogenous Accountability Collapse
12-MAY-2025
We introduce an agent-based model of $N$ interacting agents, each carrying wealth $R_i(t)$ evolving under Kou pure-jump dynamics and an accountability level $\Omega_i(t) \in [0,1]$. Three interlocking feedback loops drive the system: Loop 1 links wealth rank $r_i(t)$ to an erosion rate $\alpha(r_i) = \alpha_0 + \alpha_1 r_i^\gamma$, accelerating accountability decay at the top of the distribution; Loop 2 is an asymmetric norm-contagion process on a weighted social network, where observed impunity pulls accountability downward faster than virtue restores it; Loop 3 couples the Gini coefficient $G(t)$ to an institutional capture variable $\kappa(t)$, which weakens the social restoration mechanism and directly erodes $\Omega_i$. The full accountability dynamics are $\dot{\Omega}_i = -\alpha(r_i)\Omega_i + (1-\kappa)\,c\sum_j w_{ij}f(\Omega_j - \Omega_i) - \kappa\,\Omega_i$. Simulations reveal a phase transition at a critical Gini threshold $G^*$: below $G^*$ accountability recovers, above it the system locks into a collapse regime where the top tier reaches $\Omega \to 0$ and norm erosion propagates downward through the wealth distribution.