Abstract
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 combining and extending several components of 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 for the discussing update groups. Having one single formula allows exploring 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 discussions 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 like 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 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 to envision novel winning strategies in competing environments.
Highlights
Majoritarian social decisions have been traditionally justified by Condorcet’s jury theorem which states that, in majoritarian group decisions, the errors in individual judgment are canceled out to arbitrary accuracy as the number of voters increases
We have obtained a universal formula for the temporal evolution of agents following the Galam opinion dynamics in a parameter space of five dimensions, which are the respective proportions of inflexibles of each side, the proportion of contrarians, the mean value of shared prejudices, and the update group size
The associated opinion landscape is found to be shaped by several attractors and tipping points, which yield a rich variety of non linearities and singularities in the opinion flows
Summary
Majoritarian social decisions have been traditionally justified by Condorcet’s jury theorem which states that, in majoritarian group decisions, the errors in individual judgment are canceled out to arbitrary accuracy as the number of voters increases. Despite ongoing active research [16,17,18,19,20,21] up-to-date, the opinion dynamics issue is still lacking a comprehensive and robust framework, especially a reliable predictive tool Among those models stands the seminal Galam model [22,23,24,25,26], which combines local majority rule updates with local symmetry breaking driven by unconscious prejudices and cognitive biases in case of an even-size group at a tie. By investigating further the Galam model in a generic parameter space of five dimensions, we obtain a single universal update equation to follow the temporal evolution of opinion distribution among a heterogeneous population with any combination of rational, stubborn, and contrarian agents for any average of hidden prejudices and for an arbitrary size of groups being discussed.
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