The Degree-Dependent Threshold Model: Towards a Better Understanding of Opinion Dynamics on Online Social Networks

Abstract: With the rapid growth of online social media, people become increasingly overwhelmed by the volume and the content of the information present in the environment. The threshold model is currently one of the most common methods to capture the effect of people on others' opinions and emotions. Although many studies employ and try to improve upon the threshold model, the search for an appropriate threshold function for defining human behavior is an essential and yet unattained quest. The definition of heterogeneity in thresholds of individuals is oftentimes poorly defined, which leads to the rather simplistic use of uniform and binary functions, albeit they are far from representing the reality. In this study, we use Twitter data of size 30,704,025 tweets to mimic the adoption of a new opinion. Our results show that the threshold is not only correlated with the out-degree of nodes, which contradicts other studies but also correlated with nodes' in-degree. Therefore, we simulated two cases in which thresholds are out-degree and in-degree dependent, separately. We concluded that the system is more likely to reach a consensus when thresholds are in-degree dependent; however, the time elapsed until all nodes fix their opinions is significantly higher in this case. Additionally, we did not observe a notable effect of mean-degree on either the average opinion or the fixation time of opinions for both cases, and increasing seed size has a negative effect on reaching a consensus. Although threshold heterogeneity has a slight influence on the average opinion, the positive effect of heterogeneity on reaching a consensus is more pronounced when thresholds are in-degree dependent.