Polarization and fragmentation in social media amplify user biases, making it increasingly important to understand the evolution of opinions. Opinion dynamics provide interpretability for studying opinion evolution, yet incorporating these insights into predictive models remains challenging. This challenge arises due to the inherent complexity of the diversity of opinion fusion rules and the difficulty in capturing equilibrium states while avoiding over-smoothing. This paper constructs a unified opinion dynamics model to integrate different opinion fusion rules and generates corresponding synthetic datasets. To fully leverage the advantages of unified opinion dynamics, we introduces UniGO, a framework for modeling opinion evolution on graphs. Using a coarsen-refine mechanism, UniGO efficiently models opinion dynamics through a graph neural network, mitigating over-smoothing while preserving equilibrium phenomena. UniGO leverages pretraining on synthetic datasets, which enhances its ability to generalize to real-world scenarios, providing a viable paradigm for applications of opinion dynamics. Experimental results on both synthetic and real-world datasets demonstrate UniGO's effectiveness in capturing complex opinion formation processes and predicting future evolution. The pretrained model also shows strong generalization capability, validating the benefits of using synthetic data to boost real-world performance.

The paper studies the problem of steering multi-dimensional opinion in a social network. Assuming the society of desire consists of stubborn and regular agents, stubborn agents are considered as leaders who specify the desired opinion distribution as a distributed reward or utility function. In this context, each regular agent is seen as a follower, updating its bias on the initial opinion and influence weights by averaging their observations of the rewards their influencers have received. Assuming random graphs with reducible and irreducible topology specify the influences on regular agents, opinion evolution is represented as a containment control problem in which stability and convergence to the final opinion are proven.

In human social systems, debates are often seen as a means to resolve differences of opinion. However, in reality, debates frequently incur significant communication costs, especially when dealing with stubborn opponents. Inspired by this phenomenon, this paper examines the impact of malicious agents on the evolution of normal agents' opinions from the perspective of opinion evolution cost, and proposes corresponding solutions for the scenario in which malicious agents hold different opinions in multi-agent systems(MASs). First, this paper analyzes the negative impact of malicious agents on the opinion evolution process, reveals the additional evolution cost it brings, and provides a theoretical basis for the subsequent solutions. Secondly, based on the characteristics of opinion evolution, the malicious agent isolation algorithm based on opinion evolution direction vector is proposed, which does not strongly restrict the proportion of malicious agents. Additionally, an evolution rate adjustment mechanism is introduced, allowing the system to flexibly regulate the evolution process in complex situations, effectively achieving the trade-off between opinion evolution rate and cost. Extensive numerical simulations demonstrate that the algorithm can effectively eliminate the negative influence of malicious agents and achieve a balance between opinion evolution costs and convergence speed.

We generalize the classic multi-agent DeGroot model for opinion dynamics to incorporate the Spiral of Silence theory from political science. This theory states that individuals may withhold their opinions when they perceive them to be in the minority. As in the DeGroot model, a community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. However, agents whose current opinions are in the minority become silent (i.e., they do not express their opinion). Two models for opinion update are then introduced. In the memoryless opinion model ($\mbox{SOM}^-$), agents update their opinion by taking the weighted average of their non-silent neighbors' opinions. In the memory based opinion model ($\mbox{SOM}^+$), agents update their opinions by taking the weighted average of the opinions of all their neighbors, but for silent neighbors, their most recent opinion is considered. We show that for $\mbox{SOM}^-$ convergence to consensus is guaranteed for clique graphs but, unlike for the classic DeGroot, not guaranteed for strongly-connected aperiodic graphs. In contrast, we show that for $\mbox{SOM}^+$ convergence to consensus is not guaranteed even for clique graphs. We showcase our models through simulations offering experimental insights that align with key aspects of the Spiral of Silence theory. These findings reveal the impact of silence dynamics on opinion formation and highlight the limitations of consensus in more nuanced social models.

We generalize the DeGroot model for opinion dynamics to better capture realistic social scenarios. We introduce a model where each agent has their own individual cognitive biases. Society is represented as a directed graph whose edges indicate how much agents influence one another. Biases are represented as the functions in the square region $[-1,1]^2$ and categorized into four sub-regions based on the potential reactions they may elicit in an agent during instances of opinion disagreement. Under the assumption that each bias of every agent is a continuous function within the region of receptive but resistant reactions ($\mathbf{R}$), we show that the society converges to a consensus if the graph is strongly connected. Under the same assumption, we also establish that the entire society converges to a unanimous opinion if and only if the source components of the graph-namely, strongly connected components with no external influence-converge to that opinion. We illustrate that convergence is not guaranteed for strongly connected graphs when biases are either discontinuous functions in $\mathbf{R}$ or not included in $\mathbf{R}$. We showcase our model through a series of examples and simulations, offering insights into how opinions form in social networks under cognitive biases.

We propose an agent-based opinion formation model characterised by a two-fold novelty. First, we realistically assume that each agent cannot measure the opinion of its neighbours with infinite resolution and accuracy, and hence it can only classify the opinion of others as agreeing much more, or more, or comparably, or less, or much less (than itself) with a given statement. This leads to a classification-based rule for opinion update. Second, we consider three complementary agent traits suggested by significant sociological and psychological research: conformism, radicalism and stubbornness. We rely on World Values Survey data to show that the proposed model has the potential to predict the evolution of opinions in real life: the classification-based approach and complementary agent traits produce rich collective behaviours, such as polarisation, consensus, and clustering, which can yield predicted opinions similar to survey results.