Generalized Opinion Dynamics from Local Optimization Rules

TL;DR

This paper extends the Hegselmann-Krause opinion model by incorporating influence strength based on opinion distance, analyzing equilibrium conditions, and exploring strategic external influence, with simulations showing significant differences from traditional dynamics.

Contribution

It introduces generalized opinion update rules based on local optimization and external influence strategies, broadening understanding of opinion dynamics beyond traditional models.

Findings

Opinions converge in finite time under certain influence strength conditions.

External strategic influence can effectively modulate opinion dynamics.

Generalized models exhibit qualitatively different equilibrium behaviors.

Abstract

We study generalizations of the Hegselmann-Krause (HK) model for opinion dynamics, incorporating features and parameters that are natural components of observed social systems. The first generalization is one where the strength of influence depends on the distance of the agents' opinions. Under this setup, we identify conditions under which the opinions converge in finite time, and provide a qualitative characterization of the equilibrium. We interpret the HK model opinion update rule as a quadratic cost-minimization rule. This enables a second generalization: a family of update rules which possess different equilibrium properties. Subsequently, we investigate models in which a external force can behave strategically to modulate/influence user updates. We consider cases where this external force can introduce additional agents and cases where they can modify the cost structures for other agents. We describe and analyze some strategies through which such modulation may be possible in an order-optimal manner. Our simulations demonstrate that generalized dynamics differ qualitatively and quantitatively from traditional HK dynamics.