Interaction and self-trust based decision-making via the voting Kuramoto model

This paper develops a graph-based dynamic opinion-formation framework for group decision-making that addresses a limitation of conventional consensus-oriented models: in many real decision environments, full agreement among experts is neither realistic nor required. Existing approaches are designed to force convergence to a single consensus and therefore cannot represent settings in which persistent disagreement naturally emerges while a collective decision still needs to be made. To fill this gap, we propose a dynamical system in which experts revise their opinions through heterogeneous interpersonal influences on a general graph and individual self-trust. The resulting dynamics admit two stable and internally coherent opinion groups, enabling collective decisions to be derived from the emergent polarized structure rather than from enforced consensus. We analytically characterize the long-term behavior of the model under general network structures and illustrate its decision-making implications through simulation studies. The results show how a heterogeneous graph network shapes the formation of opinion groups and the associated collective decision. The framework thus offers a methodological tool for graph-based group decision processes in which stable disagreement, rather than full consensus, is the expected outcome. In addition, its intrinsic bipolar structure makes the framework particularly effective for identifying a single best alternative by naturally amplifying the separation between the best option and others.