Bounded Confidence Model Research Articles

BOUNDED CONFIDENCE MODEL ON GROWING POPULATIONS

This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary clusters appear erratically and include much fewer agents when the population is fixed. Through simulations, we derive the bifurcation diagram of the growing population model and compare it to the diagram obtained with an evolving probability density instead of agents, and with their equivalent having a fixed population. Our tests, when changing the usual bounded confidence function into a smooth bounded confidence function, suggest that these secondary clusters are mainly generated by a different mechanism when the population is growing than when it is fixed.

Cognitive dissonance and introversion effects on opinion dynamics and echo chamber formation

Bounded confidence models (BCM) are extensively used to model continuous opinion dynamics in social networks. Typically, these models are analysed on static networks where edges do not vary over time. Following in the footsteps of adaptive voter models, further research has considered BCMs in the setting where agents are able to dynamically adjust their edges, which subsequently feedback into the opinion dynamics of the network. Several methods of updating connections have been proposed ranging from random rewiring to more sophisticated approaches based on concordant edges, homophily and cognitive dissonance. We present a modified form of the bounded confidence model, termed the selfish agent opinion (SAO) model, where connection updates are evaluated using a general cost function. Agents in the SAO model maintain two classes of relationships, friends and acquaintances, based on which they update their opinions and edges to optimise a payoff function that may include multiple social factors. This paper explores the effects, which we describe as “cognitive dissonance” and “introversion” that attempt to mimic postulated behaviours associated with the social concepts of the same name, on social network and opinion dynamics. We find that the SAO model naturally produces echo chambers for social networks with increased sensitivity to cognitive dissonance, whilst introversion produces high levels of fragmentation and low opinion mobility. Additionally, the effect of tolerant agents and inquisitive social encounters is investigated. It is found that both the presence of very small numbers of tolerant agents and inquisitive encounters are able to strongly promote consensus formation.

Erratum: Bounded-confidence model of opinion dynamics with heterogeneous node-activity levels [Phys. Rev. Research 5 , 023179 (2023)

Erratum: Bounded-confidence model of opinion dynamics with heterogeneous node-activity levels [Phys. Rev. Research <b>5</b> , 023179 (2023)

Consensus reaching with the dynamic hybrid trust network in group decision making based on an extensive bounded confidence

This study focuses on the consensus-reaching process (CRP) in social networks. Over the years, ample research has been conducted on CRP levels. However, most feedback mechanisms do not consider the decision maker’s (DM) willingness to accept the recommendations provided by these mechanisms. Therefore, this study proposes an extensive bounded confidence-based group consensus feedback mechanism that primarily consists of two parts: (a) the construction of a hybrid dynamic trust network and (b) the construction of an extensive bounded confidence model. In the first part, we propose an algorithm to calculate the importance of network nodes and apply it to the trust propagation and aggregation process. In the second part, we propose an extensive bounded confidence model to address the limitations of existing traditional bounded confidence models. In the proposed extensive bounded confidence model, the trust threshold is no longer a “switch” to determine whether a DM interacts with other DMs but a basis to determine the strength of the DMs’ interaction; moreover, the hybrid dynamic trust relationship will determine the negotiation sets. A practical case of site selection and comparative analysis verify the effectiveness and flexibility of the proposed mechanism.

Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics

Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics

Polarized consensus-based dynamics for optimization and sampling

AbstractIn this paper we propose polarized consensus-based dynamics in order to make consensus-based optimization (CBO) and sampling (CBS) applicable for objective functions with several global minima or distributions with many modes, respectively. For this, we “polarize” the dynamics with a localizing kernel and the resulting model can be viewed as a bounded confidence model for opinion formation in the presence of common objective. Instead of being attracted to a common weighted mean as in the original consensus-based methods, which prevents the detection of more than one minimum or mode, in our method every particle is attracted to a weighted mean which gives more weight to nearby particles. We prove that in the mean-field regime the polarized CBS dynamics are unbiased for Gaussian targets. We also prove that in the zero temperature limit and for sufficiently well-behaved strongly convex objectives the solution of the Fokker–Planck equation converges in the Wasserstein-2 distance to a Dirac measure at the minimizer. Finally, we propose a computationally more efficient generalization which works with a predefined number of clusters and improves upon our polarized baseline method for high-dimensional optimization.

Агрегиране на убеждения и търсене на консенсус: логика на разногласието

The paper discusses the history of the development of different logical formalisms, explicitly modelling situations in which disagreement is present. It is structured as follows: (§1) sketches the distinction between two main traditions in logic, that have different relation to disagreement; (§2) presents Jaskowski’s discussive logic and its shortcomings; (§3) develops the doctrinal paradox in social choice theory. Then we come to (§4) the probabilistic model of Lehrer-Wagner; (§5) the bounded confidence model of Hegselmann and Krause and (§6) the agent-based model of Douven and Riegler. The aim of the paper is to show that the development of these formalisms raises many questions that are yet not solved in adequate manner.

Complex Transitions of the Bounded Confidence Model from an Odd Number of Clusters to the Next

The bounded confidence model assumes simple continuous opinion dynamics in which agents ignore opinions which are too far from their own. The two initial variants—Hegselmann–Krause (HK) and Deffuant–Weisbuch (DW)—of the model have attracted significant attention since the early 2000s. This paper revisits the version of the HK model applied to a probability distribution, earlier studied by Jan Lorenz. It shows that the bifurcation diagram depends on the parity of the size of the discretisation and that adding a small noise to the initial conditions leads to complex transitions involving several phases.

Modeling Misinformation Spread in a Bounded Confidence Model: A Simulation Study.

Misinformation has posed significant threats to all aspects of people's lives. One of the most active areas of research in misinformation examines how individuals are misinformed. In this paper, we study how and to what extent agents are misinformed in an extended bounded confidence model, which consists of three parts: (i) online selective neighbors whose opinions differ from their own but not by more than a certain confidence level; (ii) offline neighbors, in a Watts-Strogatz small-world network, whom an agent has to communicate with even though their opinions are far different from their own; and (iii) a Bayesian analysis. Furthermore, we introduce two types of epistemically irresponsible agents: agents who hide their honest opinions and focus on disseminating misinformation and agents who ignore the messages received and follow the crowd mindlessly. Simulations show that, in an environment with only online selective neighbors, the misinforming is more successful with broader confidence intervals. Having offline neighbors contributes to being cautious of misinformation, while employing a Bayesian analysis helps in discovering the truth. Moreover, the agents who are only willing to listen to the majority, regardless of the truth, unwittingly help to bring about the success of misinformation attempts, and they themselves are, of course, misled to a greater extent.

A neural probabilistic bounded confidence model for opinion dynamics on social networks

Opinion dynamics (OD) models simulate the evolution of personal opinions using computer science, social dynamics, physics, and complexity science tools on social networks. However, current opinion dynamics models mainly utilize agent-based models to simulate user interactions but still need to leverage large-scale data fully. Social networks typically involve a vast number of users and information, making it difficult for models to capture the complex interactions in real social networks. Additionally, many models overlook the specific mechanisms of user interactions, such as how network individuals influence and interact with one another, resulting in inaccuracies in modeling individual opinion evolution. This paper proposes a novel approach that integrates the probabilistic bounded confidence model (PBC) with deep learning, i.e., Neural Probabilistic Bounded Confidence (NPBC), to tackle these challenges. The NPBC model adopts an attention network, a long short-term memory (LSTM) network, and a feedforward neural network to approximate the evolution of individual opinions within networks. It satisfies the data approximation and the users’ opinion update rule that conforms to the PBC model. This model enhances the understanding of opinion dynamics, helping to develop effective strategies for opinion guidance in social networks. Finally, the proposed NPBC model is evaluated on three synthetic and Twitter datasets. The results demonstrate that the proposed NPBC model performs better than the six baseline methods in predicting user opinions. Compared to baseline models, the model’s accuracy (ACC) and comprehensive evaluation (F1) scores improve by up to 18% and 7%, respectively.

A Density Description of a Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

A Density Description of a Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

Probabilistic analysis of agent-based opinion formation models

When agent-based models are developed to capture opinion formation in large-scale populations, the opinion update equations often need to embed several complex psychological traits. The resulting models are more realistic, but also challenging to assess analytically, and hence numerical analysis techniques have an increasing importance in their study. Here, we propose the Qualitative Outcome Likelihood (QOL) analysis, a novel probabilistic analysis technique aimed to unravel behavioural patterns and properties of agent-based opinion formation models, and to characterise possible outcomes when only limited information is available. The QOL analysis reveals which qualitative categories of opinion distributions a model can produce, brings to light their relation to model features such as initial conditions, agent parameters and underlying digraph, and allows us to compare the behaviour of different opinion formation models. We exemplify the proposed technique by applying it to four opinion formation models: the classical Friedkin-Johnsen model and Bounded Confidence model, as well as the recently proposed Backfire Effect and Biased Assimilation model and Classification-based model.

A novel framework to classify opinion dynamics of mobile agents under the bounded confidence model

The formation and evolution of public opinion have been widely studied to understand how consensus forms due to atomic interactions between individuals. While many studies have paid attention to modelling influence and interaction, most of the literature assumes static agents, ignoring the frequent changes in physical locations expected in real life. This feature naturally allows humans to interact with diverse people and avoid disagreement, which heavily impacts the co-evolution of opinions, communities or isolation in human societies. Our previous work proposed an extension of the bounded confidence model inspired by the theories of homophily and cognitive dissonance, which concern humans’ natural behaviours of attraction and disagreement. Although this demonstrated a marked difference to a static opinion model and purely random mobility, the limited experiments gave little insight into the causes or the resulting structures of consensus. This article addresses these shortcomings through a thorough investigation of the impact of mobility modelled by different mechanisms. Through extensive simulation, we observe a transition from multiple stable opinion clusters to complete consensus and a shift from a geographically based organisation to isolated structure-less agents. Lastly, we propose a novel classification of the different outcomes of self-organisation in opinion models, highlighting the patterns of emerging behaviours across the spectrum of interaction range and influence parameters.

Mass media impact on opinion evolution in biased digital environments: a bounded confidence model

People increasingly shape their opinions by accessing and discussing content shared on social networking websites. These platforms contain a mixture of other users’ shared opinions and content from mainstream media sources. While online social networks have fostered information access and diffusion, they also represent optimal environments for the proliferation of polluted information and contents, which are argued to be among the co-causes of polarization/radicalization phenomena. Moreover, recommendation algorithms - intended to enhance platform usage - likely augment such phenomena, generating the so-called Algorithmic Bias. In this work, we study the effects of the combination of social influence and mass media influence on the dynamics of opinion evolution in a biased online environment, using a recent bounded confidence opinion dynamics model with algorithmic bias as a baseline and adding the possibility to interact with one or more media outlets, modeled as stubborn agents. We analyzed four different media landscapes and found that an open-minded population is more easily manipulated by external propaganda - moderate or extremist - while remaining undecided in a more balanced information environment. By reinforcing users’ biases, recommender systems appear to help avoid the complete manipulation of the population by external propaganda.

Relative opinion similarity leads to the emergence of large clusters in opinion formation models

This study considers a variant of the bounded confidence opinion formation model wherein the probability of opinion assimilation is dependent on the relative similarity of opinions. Agents are located on a social network and decide whether or not they adopt the opinion of one of the neighbors (called a role agent). Opinion assimilation is more (less) likely to occur when the distance from the opinion of the role agent is smaller (larger) than the average opinion distance from other neighbors. Thus, assimilation probability is reliant not only on opinion proximity with the role agent considered in conventional models but also on relative similarity that considers other neighbors. The simulation results demonstrate that large weights on relative similarity in determining assimilation probability increase the size of the largest opinion cluster. The size of the threshold parameter of the bounded confidence model displays inverse-U relationships with the largest cluster size. The findings imply that consideration of relative opinion similarity, as observed in recent empirical studies, prevents polarization into small opinion clusters.

Bounded-confidence model of opinion dynamics with heterogeneous node-activity levels

Bounded-confidence model of opinion dynamics with heterogeneous node-activity levels

Limit state analysis on the un-repeated multiple selection bounded confidence model

Limit state analysis on the un-repeated multiple selection bounded confidence model

Opinion Evolution with Information Quality of Public Person and Mass Acceptance Threshold.

Public persons are nodes with high attention to public events, and their opinions can directly affect the development on events. However, because of rationality, the followers' acceptance to the public persons' opinions will depend on the information trait on public persons' opinions and own comprehension. To study how different opinions of the public persons guide different followers, we build an opinion dynamics model, which would provide a theoretical method for public opinion management. Based on the classical bounded confidence model, we extract the information quality variables and individual trust threshold and introduce them to construct our two-stage opinion evolution model. And then in the simulation experiments, we analyze the different effects of opinion information quality, opinion release time, and frequency on public opinion by adjusting the different parameters. Finally, we added a case to compare real data, the data from classical model simulation and the data from improved model simulation to verify the effectiveness on our model. The research found that the more sufficient the argument and the more moderate the attitude, the more likely to guide the public opinion. If public person holds different opinions and different information quality, he should choose different time to present his opinion to achieve ideal guide effect. When public person holds neutral opinion and the information quality is relatively general, he/she can intervene in public opinion as soon as possible to control final public opinion; when public person holds extreme opinion and the information quality is relatively high, he/she can choose to express opinion after a certain period on public opinion evolution, which is conducive to improve the guidance effect on public opinion. The frequency of releasing opinions of public person consistently has a positive impact on the final public opinion.

Opinion Dynamics in Gossiper-Media Networks Based on Multiagent Reinforcement Learning

In social networks, to increase the number of followers, media express their opinions through posts, articles, and published content to cater to public preferences. Meanwhile, the evolution of public opinions is affected by both the media and peers. In this work, we investigate how the interactions between media affect the dynamics of public opinions in social networks. We propose a reinforcement learning framework to model the interactions between the public (gossipers) and media agents. We model each gossiper as an individually rational agent, which updates its opinion using the bounded confidence model (BCM). Media agents are interested in maximizing the number of following gossipers competitively, and an algorithm, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., WoLS-CALA, is proposed to achieve that goal. We analyze and experimentally verify that WoLS-CALA can learn Nash equilibria (NE) for games with continuous action space. In addition, the opinion dynamics of gossipers are theoretically analyzed, which shows that the existence of media will strengthen the consistency of gossipers' opinions. We then evaluate the framework in two synthetic networks, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., a fully connected network and a small-world network, and one real data network from Facebook. Extensive empirical simulation reveals that our framework facilitates the consensus of opinions and confirms the theoretical analysis.

How Does Persuasion Happen? A Novel Bounded Confidence Opinion Dynamics Model Based on Social Judgment Theory

Persuasion exists in every aspect of social life. It is important to understand how persuasion works and how strong it is. In this article, we improve the classic Hegselmann–Krause model, one of the most famous bounded confidence models, and propose a novel opinion dynamics model to explain the process by which persuasion occurs from a systematic perspective. In our model, the concepts of latitudes of acceptance, noncommitment, and rejection from social judgment theory and the cognitive error in the process of persuasion, namely assimilation, are introduced. When people are exchanging their opinions with their neighbors, the opinions in the latitude of acceptance will be assimilated, those in the latitude of noncommitment will keep unchanged, and those in the latitude of rejection will not be considered. Theoretical proofs show that our model will converge to a stable state in a finite time. Numerical results of extensive simulation experiments on four datasets show the performance of the model. Furthermore, real social platform data and global COVID-19 vaccination data are analyzed to verify the effectiveness of the model in the decision-making process.