Steering polarization toward consensus in signed majority-vote opinion models

Signed social networks, which encode both positive and negative relationships, frequently constrain opinion dynamics, leading to sustained polarization. We address this challenge in the signed majority-vote model by modifying the fast gradient-sign method to incorporate a uniform, sign-matched edge bias that dynamically evolves with the current opinion state. Experiments on synthetic graphs and several large real-world datasets demonstrate that a moderate level of this bias dissolves polarization and promotes broad consensus, whereas strength-matched random perturbations preserve divisions in opinion. The required bias rises with the density of antagonistic ties but is largely insensitive to network size. These results suggest that consensus in large signed networks can be restored through lightweight, structure-aware interventions, offering a feasible approach for mitigating online social division.