When Small Acts Scale: Ethical Thresholds in Network Diffusion

TL;DR

The paper shows that ethical evaluation, which often focuses on dyadic interactions, can substantially misestimate responsibility when actions diffuse through networks. It introduces a minimal diffusion framework with baseline weight $w$ and parameters $b$ (branching), $\alpha$ (per-hop attenuation), $q$ (compliance), and horizon $d$, yielding a closed-form network multiplier and a critical threshold $r = b\alpha q = 1$. The analysis identifies subcritical, critical, and supercritical regimes, revealing when small acts saturate, scale linearly, or cascade geometrically, and offers concrete design levers to influence diffusion. Through worked examples and public-health applications (pandemic mitigation and vaccination), the framework demonstrates how platform design and policy decisions can dramatically alter downstream responsibility and norm spread, highlighting cascade-aware governance as a practical priority.

Abstract

Much ethical evaluation treats actions dyadically: one agent acts on one recipient. In networked, platform-mediated environments, this lens misses how public acts diffuse. We introduce a minimal message-passing model in which an initiating act with baseline valence w spreads across a social graph with exposure b, per-hop salience $alpha$, compliance $q$, and depth (horizon) d. The model yields a closed-form \emph{network multiplier} relative to the dyadic baseline and identifies a threshold at r=b.alpha.q=1 separating subcritical (saturating), critical (linear), and supercritical (geometric) regimes. We show how common platform design levers -- reach and fan-out (affecting b), ranking and context (affecting alpha), share mechanics and friction (affecting q), and time-bounds (affecting d) -- systematically change expected downstream responsibility Applications include pandemic mitigation and vaccination externalities, as well as platform amplification of prosocial and harmful norms.