# Asynchronous Opinion Dynamics in Social Networks

arXiv: https://arxiv.org/abs/2201.12923 · HTML: https://mlsanity.com/paper/2201.12923/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2022.

## Built on by (most cited first, 2 of 2)

- [Random Majority Opinion Diffusion: Stabilization Time, Absorbing States, and Influential Nodes](https://mlsanity.com/paper/2302.06760/) (2023)
- [On the Role of Memory in Robust Opinion Dynamics](https://mlsanity.com/paper/2302.08600/) (2023)

## Abstract (arXiv)

Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own. The system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not mboxinfluence each other. We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of O(n|E|2 (varepsilon/δ)2) on the expected number of opinion updates until convergence, where |E| is the number of edges of the social network. For the complete social network we show a bound of O(n3(n2 + (varepsilon/δ)2)) that represents a major improvement over the previously best upper bound of O(n9 (varepsilon/δ)2). Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.