Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

Abstract

This paper introduces a general model of opinion dynamics with opinion-dependent connectivity. Agents update their opinions asynchronously: for the updating agent, the new opinion is the average of the k closest opinions within a subset of m agents that are sampled from the population of size n. Depending on k and m with respect to n, the dynamics can have a variety of equilibria, which include consensus and clustered configurations. The model covers as special cases a classical gossip update (if m = n) and a deterministic update defined by the k nearest neighbors (if m = k). We prove that the dynamics converges to consensus if n > 2(m − k). Before convergence, however, the dynamics can remain for long time in the vicinity of metastable clustered configurations.

Asymptotically stable polarization of multi-agent gradient flows over manifolds

“…As noted in §2.2, we may use signed graphs for intergroup antagonism, then (2) and ( 4) would respectively reduce in form to (5) and (6). And the same conclusion as Prop.…”

“…This is a typical distributed process [1], and is akin to many aspects of social opinion formation, as numerous observers in the systems and control community have identified [2,3]. Accordingly, insights on multi-agent systems, especially on the stability and convergence properties of consensus, have been aptly applied to a dizzying array of opinion dynamics models to study social agreement [4,5,6]. Continuing this tradition, we investigate multi-agent systems that evolve over nonlinear spaces for another type of emergent behavior, namely, polarization.…”

Generalized solutions to opinion dynamics models with discontinuities

“…This model was first pointed out in [4], while several other models of opinion dynamics and collective motion have considered topological interactions: see [19,40] and references therein.…”

The Closed Loop Between Opinion Formation and Personalized Recommendations

“…Platform effects have also been explored by agent-based models in relation to filter bubbles [22] and polarization [23]. In the filter bubble perspective, the platform could restrict the interactions of the users to a limited number of most similar individuals: our recent paper [24] investigates a simple opinion model based on this idea.…”