Deffuant bounded-confidence model — agents only influence each other when their opinions are close enough
The Deffuant model (2000) is the simplest bounded-confidence model of opinion formation. Each agent holds a real-valued opinion x ∈ [0, 1]. At each step, two agents are chosen at random. If |xi − xj| < ε (the confidence threshold), both shift toward each other by a fraction μ of their difference. If they are further apart, nothing happens.
Small ε → agents only talk to like-minded people → echo chambers and political polarisation. Large ε → everyone is within tolerance → global consensus. Intermediate ε produces a fixed number of opinion clusters matching the rule ≈ 1/(2ε).
The media bias slider adds a persistent external nudge: a virtual media agent with fixed opinion pulls susceptible agents slightly toward it every step — modelling the influence of mass media or social-media feed algorithms.