In most existing linguistic distribution multiple criteria group decision-making (MCGDM) models, the sample size of group linguistic distribution assessment (LDA) is often neglected, and the decision makers are viewed to be independent. The probabilistic distribution is closely related to the sample size, and there exist more or fewer interference effects among different individual opinions. Thus, this article develops a quantum framework for modeling interference effects in the linguistic distribution MCGDM process. First, considering the sample size information, we redefine the LDAs and provide a new computational model for them. Second, to integrate a series of LDAs, the linguistic distribution weighted averaging (LDWA) operator is presented. Mathematic proofs reveal that the new LDWA operator can not only ensure the information integrality but also can avoid the conjunctive and disjunctive operations. Third, to explore the interference effects among individual opinions, a quantum framework is constructed. In this process, individual opinions are viewed as various wave functions occurring synchronously. They interfere with each and influence the aggregation result. Finally, an illustrative example of Internet finance soft power evaluation is provided to verify the effectiveness. Sensitivity and comparative analyses are also implemented to assess the stability and validity of our method.