Stochastic Bounded Confidence Opinion Dynamics: Towards characterizing opinion differences in finite time

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Name of the Speaker: Sushmitha Shree S (EE18D702)
Guide: Dr. Krishna Jagannathan
Co-Guide: Dr. Avhishek Chatterjee
Venue/Online meeting link: ESB-244 (Seminar Hall)
Date/Time: 14th December 2022 (Wednesday), 11:00 AM

With the extensive use of online social networks that enable large-scale opinion exchanges, the study of opinion dynamics has gained more importance. In classical opinion dynamics, an agent updates its opinion based on its neighbors on a social graph or the proximity of its opinion with others. Linear dynamics capture graph-based interactions, and bounded confidence dynamics capture pairwise opinion-dependent interactions. Stochastic bounded confidence (SBC) dynamics is a recent framework that generalizes classical dynamics by modeling the inherent stochasticity and noise (errors) in real-world opinion exchanges. The asymptotic behavior of these dynamics has already been studied in the literature. However, the findings do not shed light on their behavior in finite time, which is often of interest in practice.

In this work, we characterize the evolution of opinions over a finite time period. We focus primarily on characterizing the finite time behavior of SBC dynamics of two agents and on a bistar graph. Such dynamics closely model bipartisan democratic societies with two leaders/ parties with large followings. In particular, we derive high-probability bounds for the opinion difference between two agents and demonstrate a strong concentration of opinion difference around zero under the conditions that lead to asymptotic stability of the dynamics. This work is crucial for analyzing general multi-agent dynamics.