# Tipping points in opinion dynamics: a universal formula in five dimensions

## TL;DR

This paper introduces a universal five-dimensional formula that predicts opinion dynamics, including sudden minority opinion outbreaks, by analyzing the social landscape and its attractors, enabling forecasts of major societal events.

## Contribution

The paper extends the Galam model into a unified five-dimensional formula, capturing diverse individual traits and group sizes to predict opinion shifts and tipping points.

## Key findings

- Predicts minority opinion outbreaks and major societal events.
- Unveils the geometry of opinion dynamics landscape.
- Enables forecasting of social and political outcomes.

## 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.