When Small Acts Scale: Ethical Thresholds in Network Diffusion

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.