Sudden Trust Collapse in Networked Societies

TL;DR

This paper models how trust in networks can suddenly collapse due to amplification effects, showing that trust dynamics can exhibit phase transitions with multiple stable states and spontaneous shifts.

Contribution

It introduces a stylized model demonstrating first order phase transitions in trust, including coexistence of high and low trust states and the possibility of spontaneous trust collapse.

Findings

Trust can undergo sudden, catastrophic collapse without external shocks.

Multiple equilibrium states exist, including high-trust and low-trust configurations.

Large systems show history dependence, with initial conditions determining trust state.

Abstract

Trust is a collective, self-fulfilling phenomenon that suggests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in networks, which generically displays a first order transition. The basic assumption of our model is that whereas trust begets trust, panic also begets panic, in the sense that a small decrease in trust may be amplified and ultimately lead to a sudden and catastrophic drop of trust. We show, using both numerical simulations and mean-field analytic arguments, that there are extended regions of the parameter space where two equilibrium states coexist: a well-connected network where confidence is high, and a poorly connected network where confidence is low. In these coexistence regions, spontaneous jumps from the well-connected state to the poorly connected state can occur, corresponding to a sudden collapse of trust that is not caused by any major external catastrophe. In large systems, spontaneous crises are replaced by history dependence: whether the system is found in one state or in the other essentially depends on initial conditions. Finally, we document a new phase, in which agents are connected yet distrustful.