Mathematical models of message discrepancy: previous models and a modified psychological discounting model

Formal modeling is rare in communication studies. Still, several mathematical models have been proposed regarding the persuasive effects of message discrepancy, the difference between a message’s advocated position and a message recipient’s initial position. With numerical simulations, we analyzed four formal models to identify their strengths and weaknesses. Based on analyses of previous models, we proposed a modified psychological discounting model by solving a differential equation regarding the rate of change of the probability of message acceptance with respect to psychological discrepancy. Whereas previous models predicted nonmonotonic relationships between message discrepancy and belief change, the new model predicts that as message discrepancy increases, belief change monotonically increases unless facilitating factors change due to extremely discrepant messages. We discuss differences between the previous models and the new model, and their significance and implications for theories of persuasion as well as the limitations of the new model.