DeffuantWeisbuch

The Deffuant‑Weisbuch model is a simple, agent‑based framework for simulating the evolution of continuous opinions within a population. It was introduced in 2000 by Pierre Deffuant, Réka Weisbuch, and collaborators in a paper titled “Mixing laws in the evolution of a continuous distribution of opinions”. In the model, each individual occupies a point on the real line representing a continuous opinion on a topic of interest.

At each time step a pair of individuals is selected at random. If the distance between their opinions is smaller than a predefined confidence bound (ε), the pair interacts and each updates their opinion by moving a fraction (μ) towards the other’s value. If the distance exceeds ε, no interaction occurs. Over many iterations, this simple rule leads to the emergence of consensus, polarization, or fragmentation, depending on the values of ε and μ. A small confidence bound tends to generate multiple opinion clusters, while a large confidence bound encourages global consensus.

The model has been widely adopted in the field of sociophysics to study how local interactions and bounded confidence shape collective opinion patterns. It has been extended in various ways, incorporating heterogeneous confidence bounds, network topologies, and stochastic noise. Empirical studies have used the model to fit data on public opinion and voting behavior. Despite its simplicity, the Deffuant‑Weisbuch model remains a foundational tool for researchers exploring the mathematical properties of opinion dynamics and the mechanisms that drive social coordination.