  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.
