Regimes of Influence under Trust-Distrust Gating

Abstract

In many social communities, individuals can simultaneously trust and distrust the same source, a feature standard opinion-dynamics models often ignore. We formalize this ambivalence with Gated Network Credence, in which each directed relationship encodes distinct trust and distrust assessments. These jointly determine "net trust" -- the willingness to rely on a source -- and "uncertainty" -- the conflict between trust and distrust within the same relationship. Agents update beliefs only when net trust exceeds a threshold and uncertainty falls below another, yielding an effective influence graph whose topology drives long-run belief states. Sweeping both thresholds uncovers four regimes -- Accommodating, Evaluative, Friction-averse, and Guarded -- that differ in openness to trust and conflict. Under the modeled family of trust-distrust coupling and prestige-biased trust allocation, the model exhibits a hub-periphery reversal: in the Evaluative regime, high-degree agents contribute more strongly to the limiting belief, whereas in the Friction-averse regime, stringent uncertainty filtering can disproportionately remove hub-directed influence channels and reduce their contribution to the collective equilibrium. This conditional pattern recurs across synthetic network topologies and two empirical network evaluations. Our results show that belief dynamics depend not only on network structure but also on how relational ambivalence between trust and distrust gates interpersonal influence.