Opinion dynamics in a three-choice system

TL;DR

This paper extends Galam's opinion spreading model to three choices, analyzing how opinions evolve and dominate in a population with probabilistic tie-breaking, revealing rapid polarization and minority invasion scenarios.

Contribution

It introduces a three-choice opinion model with probabilistic tie-breaking and derives phase diagrams and dynamics through analysis and simulations.

Findings

Polarization occurs rapidly in the system.

Small minority opinions can dominate under certain conditions.

The model provides insights into multi-choice opinion dynamics.

Abstract

We generalize Galam's model of opinion spreading by introducing three competing choices. At each update, the population is randomly divided in groups of three agents, whose members adopt the opinion of the local majority. In the case of a tie, the local group adopts opinion A, B or C with probabilities alpha, beta and (1-alpha-beta) respectively. We derive the associated phase diagrams and dynamics by both analytical means and simulations. Polarization is always reached within very short time scales. We point out situations in which an initially very small minority opinion can invade the whole system.