Opinion Formation by Voter Model with Temporal Decay Dynamics

Social networks play an important role for spreading information and forming opinions. A variety of voter models have been defined that help analyze how people make decisions based on their neighbors' decisions. In these studies, common practice has been to use the latest decisions in opinion formation process. However, people may decide their opinions by taking account not only of their neighbors' latest opinions, but also of their neighbors' past opinions. To incorporate this effect, we enhance the original voter model and define the temporal decay voter (TDV) model incorporating a temporary decay function with parameters, and propose an efficient method of learning these parameters from the observed opinion diffusion data. We further propose an efficient method of selecting the most appropriate decay function from among the candidate functions each with the optimized parameter values. We adopt three functions as the typical candidates: the exponential decay, the power-law decay, and no decay, and evaluate the proposed method (parameter learning and model selection) through extensive experiments. We, first, experimentally demonstrate, by using synthetic data, the effectiveness of the proposed method, and then we analyze the real opinion diffusion data from a Japanese word-of-mouth communication site for cosmetics using three decay functions above, and show that most opinions conform to the TDV model of the power-law decay function.