Bias, belief, and consensus: Collective opinion formation on fluctuating networks

Generalized naming game and Bayesian naming game as dynamical systems

We study the β model (β-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the β model, we demonstrate the existence of a nongeneric bifurcation with a bifurcation point β_{c}=1/3. As β passes through β_{c}, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities p_{A} and p_{B} as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that p_{A}=p_{B}=p, where p is a constant.

Analytic Versus Computational Cognitive Models: Agent-Based Modeling as a Tool in Cognitive Sciences

Computational cognitive models typically focus on individual behavior in isolation. Models frequently employ closed-form solutions in which a state of the system can be computed if all parameters and functions are known. However, closed-form models are challenged when used to predict behaviors for dynamic, adaptive, and heterogeneous agents. Such systems are complex and typically cannot be predicted or explained by analytical solutions without application of significant simplifications. In addressing this problem, cognitive and social psychological sciences may profitably use agent-based models, which are widely employed to simulate complex systems. We show that these models can be used to explore how cognitive models scale in social networks to calibrate model parameters, to validate model predictions, and to engender model development. Agent-based models allow for controlled experiments of complex systems and can explore how changes in low-level parameters impact the behavior at a whole-system level. They can test predictions of cognitive models and may function as a bridge between individually and socially oriented models.

Large networks of rational agents form persistent echo chambers

Echo chambers (ECs) are enclosed epistemic circles where like-minded people communicate and reinforce pre-existing beliefs. It remains unclear if cognitive errors are necessarily required for ECs to emerge, and then how ECs are able to persist in networks with available contrary information. We show that ECs can theoretically emerge amongst error-free Bayesian agents, and that larger networks encourage rather than ameliorate EC growth. This suggests that the network structure itself contributes to echo chamber formation. While cognitive and social biases might exacerbate EC emergence, they are not necessary conditions. In line with this, we test stylized interventions to reduce EC formation, finding that system-wide truthful ‘educational’ broadcasts ameliorate the effect, but do not remove it entirely. Such interventions are shown to be more effective on agents newer to the network. Critically, this work serves as a formal argument for the responsibility of system architects in mitigating EC formation and retention.