Expressed and private opinion dynamics in signed networks based on path-dependence framework

Opinion evolution in social networks represents a complex dynamical process, particularly when accounting for the interplay between expressed and private opinions-a dynamic that captures the tension between social conformity and individual authenticity. In this paper, we examine the evolution of these two opinion types in signed networks using the expressed and private opinion (EPO) model, in which each individual carries distinct expressed and private opinions. By applying the lifting technique to the EPO model, we rigorously address the influence of negative edges, while the path-dependence theory is employed to model transitions between consecutive topics. Through analytical study, we derive sufficient conditions to eliminate discrepancies between expressed and private opinions across a sequence of topics, ensuring convergence to zero consensus, bipartite consensus, or bounded opinion stability. Notably, iterative topic discussions lead to asymptotic alignment between private and expressed opinions, with all trajectories confined within a well-defined range. Furthermore, for structurally unbalanced networks, we establish a sufficient condition guaranteeing bipartite consensus. Numerical simulations validate all theoretical findings.