Abstract

I will present a general model of continuous-time opinion dynamics for an arbitrary number of agents that sense or communicate over a network and form real-valued opinions about an arbitrary number of options. Drawing from biology, physics, and social psychology, an attention parameter is introduced to modulate social influence and a saturation function to bound inter-agent and intra-agent opinion exchanges. This yields simply parameterized dynamics that exhibit the range of opinion formation behaviors predicted by model-independent bifurcation theory but not exhibited by linear models or existing nonlinear models. Behaviors include rapid and reliable formation of multistable consensus and dissensus states, even in homogeneous networks, as well as ultra-sensitivity to inputs, robustness to uncertainty, flexible transitions between consensus and dissensus, and opinion cascades. Augmenting the opinion dynamics with feedback dynamics for the attention parameter results in tunable thresholds that govern sensitivity and robustness. The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision making and dynamic task allocation. This is joint work with Alessio Franci (UNAM, Mexico) and Anastasia Bizyaeva (Princeton). The talk is based on version 2 of the paper “A General Model of Opinion Dynamics with Tunable Sensitivity”, which will be available on Tuesday October 13, 2020 here: https://arxiv.org/abs/2009.04332v2