Tipping Points In Opinion Dynamics: A Universal Formula In Five Dimensions

A universal formula is shown to predict the dynamics of public opinion including eventual sudden and unexpected outbreaks of minority opinions within a generic parameter space of five dimensions. The formula is obtained by combining and extending several components of the Galam model of opinion dynamics, otherwise treated separately, into one single update equation, which then deploys in a social space of five dimensions. Four dimensions account for a rich diversity of individual traits within a heterogeneous population, including differentiated stubbornness, contrarianism, and embedded prejudices. The fifth dimension is the size of the update groups being discussed. Having one single formula allows one to explore the complete geometry of the underlying landscape of opinion dynamics. Attractors and tipping points, which shape the topology of the different possible dynamics flows, are unveiled. Driven by repeated discussion among small groups of people during a social or political public campaign, the phenomenon of minority spreading and parallel majority collapse are thus revealed ahead of their occurrence. Accordingly, within the opinion landscape, unexpected and sudden events such as Brexit and Trump victories become visible within a forecast time horizon, making them predictable. Despite the accidental nature of the landscape, evaluating the parameter values for a specific case allows one to single out which basin of attraction is going to drive the associate dynamics, and thus, a prediction of the outcome becomes feasible. The model may apply to a large spectrum of social situations including voting outcomes, market shares, and societal trends, allowing us to envision novel winning strategies in competing environments.