Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation

TLDR

Opinion dynamics can lead to consensus, polarization, or fragmentation depending on interaction rules. The study examines continuous opinion dynamics models using analytical techniques and simulations. The authors develop a unified framework covering classical consensus, Friedkin–Johnsen, time‑dependent, and nonlinear bounded‑confidence models, and perform extensive simulations of the nonlinear variant, supported by an appendix of mathematical definitions and theorems. Section 3 reports key analytical findings for each model.

Abstract

When does opinion formation within an interacting group lead to consensus, polarization or fragmentation? The article investigates various models for the dynamics of continuous opinions by analytical methods as well as by computer simulations. Sec- tion 2 develops within a unified framework the classical model of consensus formation, the variant of this model due to Friedkin and Johnsen, a time-dependent version and a nonlinear version with bounded confidence of the agents. Section 3 presents for all these models major analytical results. Section 4 gives an extensive exploration of the nonlinear model with bounded confidence by a series of computer simulations. An ap- pendix supplies needed mathematical definitions, tools, and theorems.