Institutional Harm through Threshold Cascades

Can a population of people not individually inclined to harm others nonetheless produce harmful collective outcomes, purely because of the institutional structure they inhabit? Social scientists have long argued yes, but existing accounts are largely qualitative and provide no precise condition distinguishing safe institutions from unsafe ones. We develop a threshold cascade model in which agents have positive activation thresholds, harmful behavior is irreversible, and the institution exerts both standing pressure and peer influence along a weighted network. We give a necessary and sufficient condition, checkable from the institution's structure and its members' thresholds, for resistance to any shock up to a given size. The criterion extends to signed influence, in which some peer effects counteract harm, and yields a convex optimization formulation for least-cost repair. It also reveals a sharp frontier between functionality and safety. An institution can coordinate its members and remain safe if and only if the exposure that coordination creates stays below the weakest member's net threshold. A further tension arises when coordination requires responsiveness to peer influence, which can make it impossible to prevent the most exposed group from cascading. We then analyze a mean-field model of two groups differing in how easily their members are pushed into harm. When one group is unstable in isolation but the system is stable under full mixing, disproportionate within-group influence creates a sharp homophily threshold beyond which the harm-free state becomes unstable. In the model, identical treatment of both groups does not generally equalize their cascade robustness.