Micro-foundation of opinion dynamics: Rich consequences of the weighted-median mechanism

Abstract

The key to obtaining a mechanistic and reliable understanding of complex public opinion formation processes is to identify the main mechanism governing interpersonal influence. Researchers have long been exploring simple yet predictive mathematical models of opinion dynamics. Although most models are based on the assumption that individuals update their opinions by averaging others' opinions, researchers might need to rethink this universally adopted micro-foundation. The deceivingly simple weighted-averaging mechanism features a non-negligible unrealistic implication, which brings unnecessary difficulties in seeking a proper balance between model complexity and predictive power. In this paper, we fundamentally resolve this problem by proposing the weighted-median mechanism as a new micro-foundation of opinion dynamics. Such an inconspicuous change from averaging to median leads to rich consequences. The weighted-median mechanism, derived from the cognitive dissonance theory in psychology, is well supported by online experiment data. It also broadens the applicability of opinion dynamics models to multiple-choice issues with ordered discrete options, e.g., political elections. Moreover, comparative studies show that the weighted-median mechanism predicts various real-world patterns of opinion evolution while some widely studied averaging-based models fail to, including how group structure affects the likelihood of reaching consensus and how extreme opinions are located in social networks.