With the rapid growth of online social media, people become increasingly overwhelmed by the volume and the content of the information present in the environment. The threshold model is currently one of the most common methods to capture the effect of people on others' opinions and emotions. Although many studies employ and try to improve upon the threshold model, the search for an appropriate threshold function for defining human behavior is an essential and yet unattained quest. The definition of heterogeneity in thresholds of individuals is oftentimes poorly defined, which leads to the rather simplistic use of uniform and binary functions, albeit they are far from representing the reality. In this study, we use Twitter data of size 30,704,025 tweets to mimic the adoption of a new opinion. Our results show that the threshold is not only correlated with the out-degree of nodes, which contradicts other studies but also correlated with nodes' in-degree. Therefore, we simulated two cases in which thresholds are out-degree and in-degree dependent, separately. We concluded that the system is more likely to reach a consensus when thresholds are in-degree dependent; however, the time elapsed until all nodes fix their opinions is significantly higher in this case. Additionally, we did not observe a notable effect of mean-degree on either the average opinion or the fixation time of opinions for both cases, and increasing seed size has a negative effect on reaching a consensus. Although threshold heterogeneity has a slight influence on the average opinion, the positive effect of heterogeneity on reaching a consensus is more pronounced when thresholds are in-degree dependent.
The process of opinion formation through synthesis and contrast of different viewpoints has been the subject of many studies in economics and social sciences. Today, this process manifests itself also in online social networks and social media. The key characteristic of successful promotion campaigns is that they take into consideration such opinion-formation dynamics in order to create a overall favorable opinion about a specific information item, such as a person, a product, or an idea. In this paper, we adopt a well-established model for social-opinion dynamics and formalize the campaign-de…
Social media and social networking sites have become a global pinboard for exposition and discussion of news, topics, and ideas, where social media users often update their opinions about a particular topic by learning from the opinions shared by their friends. In this context, can we learn a data-driven model of opinion dynamics that is able to accurately forecast opinions from users? In this paper, we introduce SLANT, a probabilistic modeling framework of opinion dynamics, which represents users opinions over time by means of marked jump diffusion stochastic differential equations, and allow…
Most previous works on opinion modeling lack the simultaneous study of individual mental activity and group behavior. This paper is motivated to propose an agent-based online opinion formation model based on attitude change theory, group behavior theory and evolutionary game theory in the perspective of sociology and psychology. In this model, there are three factors influencing the persuasion process, including credibility of the leaders, characteristic of the recipient, and group environment. The proposed model is applied to Twitter to analyze the influence of topic type, parameter changing,…
Recent years saw an increased interest in modeling and understanding the mechanisms of opinion and innovation spread through human networks. Using analysis of real-world social data, researchers are able to gain a better understanding of the dynamics of social networks and subsequently model the changes in such networks over time. We developed a social network model that both utilizes an agent-based approach with a dynamic update of opinions and connections between agents and reflects opinion propagation and structural changes over time as observed in real-world data. We validate the model usi…
Understanding the evolution of collective beliefs is of critical importance to get insights on the political trends as well as on social tastes and opinions. In particular, it is pivotal to develop analytical models that can predict the beliefs dynamics and capture the interdependence of opinions on different subjects. In this paper we tackle this issue also accounting for the individual endogenous process of opinion evolution, as well as repulsive interactions between individuals' opinions that may arise in the presence of an adversarial attitude of the individuals. Using a mean field approac…
The dissemination of information and the development of public opinion are essential elements of most social media platforms and are often described as distinct, man-made occurrences. However, what is often disregarded is the interdependence between these two phenomena. Information dissemination serves as the foundation for the formation of public opinion, while public opinion, in turn, drives the spread of information. In our study, we model the co-evolutionary relationship between information and public opinion on heterogeneous multiplex networks. This model takes into account a minority of …
We proposed a new model, which capture the main difference between information and opinion spreading. In information spreading additional exposure to certain information has a small effect. Contrary, when an actor is exposed to 2 opinioned actors the probability to adopt the opinion is significant higher than in the case of contact with one such actor (called by J. Kleinberg "the 0-1-2 effect"). In each time step if an actor does not have an opinion, we randomly choose 2 his network neighbors. If one of them has an opinion, the actor adopts opinion with some low probability, if two - with a hi…
Opinion leaders are ubiquitous in both online and offline social networks, but the impacts of opinion leaders on social behavior contagions are still not fully understood, especially by using a mathematical model. Here we generalize the classical Watts threshold model and address the influences of the opinion leaders, where an individual adopts a new behavior if one of his/her opinion leaders adopts the behavior. First, we choose the opinion leaders randomly from all individuals in the network and find the impacts of opinion leaders make other individuals adopt the behavior more easily. Specif…
Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for the asymmetric influences in relationships among individuals in a social group. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We hav…
The SARS-CoV-2 pandemic reminded us how vaccination can be a divisive topic on which the public conversation is permeated by misleading claims, and thoughts tend to polarize, especially on online social networks. In this work, motivated by recent natural language processing techniques to systematically extract and quantify opinions from text messages, we present a differential framework for bivariate opinion formation dynamics that is coupled with a compartmental model for fake news dissemination. Thanks to a mean-field analysis we demonstrate that the resulting Fokker-Planck system permits to…
Trust assessment plays a key role in many online applications, such as online money lending, product reviewing and active friending. Trust models usually employ a group of parameters to represent the trust relation between a trustor-trustee pair. These parameters are originated from the trustor's bias and opinion on the trustee. Naturally, these parameters can be regarded as a vector. To address this problem, we propose a framework to accurately convert the single values to the parameters needed by 3VSL. The framework firstly employs a probabilistic graph model (PGM) to derive the trustor's op…
Empirical studies are inconclusive about the underlying mechanisms that shape the interrelated dynamics of opinions and interpersonal attraction. There is strong evidence that others whom are liked have a positive influence on opinions and similarities induce attraction (homophily). We know less about "negative" mechanisms concerning whether disliked others induce shifts away from consensus (negative influence), whether large differences (dissimilarity) generate distancing, and whether dissimilarities induce disliking (heterophobia). This study tests discriminating hypotheses about the presenc…
The goal of opinion maximization is to maximize the positive view towards a product, an ideology or any entity among the individuals in social networks. So far, opinion maximization is mainly studied as finding a set of influential nodes for fast content dissemination in a social network. In this paper, we propose a novel approach to solve the problem, where opinion maximization is achieved through efficient information spreading. In our model, multiple sources inject information continuously into the network, while the regular nodes with heterogeneous social learning abilities spread the info…
Network dynamics has always been a meaningful topic deserving exploration in the realm of academy. previous network models contain two parts: (1) generating structure as per user property; (2) changing property as per network structure. Properties in these models, however, cannot be interpreted to concept in prevalent social theories or empirical truth. Also, they usually treat everyone in an uniform fashion. While such assumption is quite misguiding, and thus saliently limits their performance. To overcome these flaws, we devise a personalized evolving model for social network and opinion (PE…
We investigate the impact of noise and topology on opinion diversity in social networks. We do so by extending well-established models of opinion dynamics to a stochastic setting where agents are subject both to assimilative forces by their local social interactions, as well as to idiosyncratic factors preventing their population from reaching consensus. We model the latter to account for both scenarios where noise is entirely exogenous to peer influence and cases where it is instead endogenous, arising from the agents' desire to maintain some uniqueness in their opinions. We derive a general …
Research interest on Online Social Networks (OSNs), has increased dramatically over the last decade, mainly because online networks provide a vast source of social information. Graph structure, user connections, growth, information exposure and diffusion, are some of the most frequently researched subjects. However, some areas of these networks, such as anonymity, equality and bias are overlooked or even unconsidered. In the related bibliography, such features seem to be influential to social interactions. Based on these studies, we aim at determining how universal anonymity affects bias, user…
Among the several approaches that have been attempted at studying opinion dynamics, the Sznajd model provides some particularly interesting features, such as its simplicity and ability to represent some of the mechanisms believed to be involved in opinion dynamics. The standard Sznajd model at zero temperature is characterized by converging to one stable state, implying null diversity of opinions. In the present work, we develop an approach -- namely the adaptive Sznajd model -- in which changes of opinion by an individual (i.e. a network node) implies in possible alterations in the network to…
We introduce and discuss kinetic models of opinion formation on social networks in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion formation model is subsequently coupled with a kinetic model describing the spreading of popularity of a product on the web through a social network. Numerical experiments on the underlying kinetic models show a good qualitative agreement with some measured trends of hashtags on social media websites and illustrate how companies can take advantage of the network structure to obtain at best the advertisemen…
In this paper, the effect on collective opinions of filtering algorithms managed by social network platforms is modeled and investigated. A stochastic multi-agent model for opinion dynamics is proposed, that accounts for a centralized tuning of the strength of interaction between individuals. The evolution of each individual opinion is described by a Markov chain, whose transition rates are affected by the opinions of the neighbors through influence parameters. The properties of this model are studied in a general setting as well as in interesting special cases. A general result is that the ov…
Quantifying opinion homophily in online social networks: A bounded confidence perspective
School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；Division of Automatic Control, Department of Electrical Engineering, Linköping University（林雪平大学电气工程学院自动控制系）；Department of Electrical Engineering and Information Technology, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学电气与信息工程系）；Department of Engineering, University of Sannio（桑尼奥大学工程系）；Institute of Information Science and Technologies “A. Faedo” (ISTI), National Research Council (CNR)（意大利国家研究委员会“阿·法多”信息技术研究所）；College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机科学与软件工程学院）
We propose a modified Vicsek-like model to study influence dynamics and opinion formation in social networks. We work on the premise that opinions of members of a group may be considered to be analogous to the direction of motion of a particle in space. The opinions are susceptible to change under the influence of familiar individuals who maintain similar beliefs. This is unlike the bounded-confidence models which solely rely on interactions based on closeness of opinions. The influence network evolves either when similar-minded individuals acquaint or when they fall out over their beliefs. Th…
In this paper, the influence of the social media on the opinion formation process is modeled during an election campaign. In the proposed model, peer- to-peer interactions and targeted online propaganda messages are assumed to be the driving forces of the opinion formation dynamics. The conviction power of the targeted messages is based on the collected and processed private information. In this work, the model is based on an artificial society, initially evenly divided between two parties. The bounded confidence model governs peer-to-peer interactions with a value of confidence parameter whic…
Much recent research on social networks has focused on the modeling and analysis of how opinions evolve as a function of interpersonal relationships. It is also of great interest to model and understand the implications of friendly and antagonistic relationships. In this paper, we propose a new, simple and intuitive model that incorporates the socio-psychological phenomenon of the boomerang effect in opinion dynamics. We establish that, under certain conditions on the structure of the signed network that corresponds to the so-called structural balance property, the opinions in the network pola…
The classic influence maximization problem finds a limited number of influential seed users in a social network such that the expected number of influenced users in the network, following an influence cascade model, is maximized. The problem has been studied in different settings, with further generalization of the graph structure, e.g., edge weights and polarities, target user categories, etc. In this paper, we introduce a unique influence diffusion scenario involving a population that split into two distinct groups, with opposing views. We aim at finding the top-$k$ influential seed nodes so…
Pre-Construction of Opinion Dynamics Considering Structural Inequality: Interdisciplinary Analysis of Complex Social Stratification, Media Influence, and Functionalism
Public opinion polling is usually done by random sampling from the entire population, treating individual opinions as independent. In the real world, individuals' opinions are often correlated, e.g., among friends in a social network. In this paper, we explore the idea of partitioned sampling, which partitions individuals with high opinion similarities into groups and then samples every group separately to obtain an accurate estimate of the population opinion. We rigorously formulate the above idea as an optimization problem. We then show that the simple partitions which contain only one sampl…
Social media has become an emerging alternative to opinion polls for public opinion collection, while it is still posing many challenges as a passive data source, such as structurelessness, quantifiability, and representativeness. Social media data with geotags provide new opportunities to unveil the geographic locations of users expressing their opinions. This paper aims to answer two questions: 1) whether quantifiable measurement of public opinion can be obtained from social media and 2) whether it can produce better or complementary measures compared to opinion polls. This research proposes…
Passive consumption of a quantifiable amount of social media information related to a topic can cause individuals to form opinions. If a substantial amount of these individuals are motivated to take action from their recently established opinions, a movement or public opinion shift can be induced independent of the information's veracity. Given that social media is ubiquitous in modern society, it is imperative that we understand the threshold at which social media data results in opinion formation. The present study estimates population opinion formation thresholds by querying 2222 participan…
We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of Universities of Cambridge and Oxford, LiveJournal and Twitter. In this model the opinion formation of linked electors is weighted with their PageRank probability. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion to a significant fraction of the society. However, for a homogeneous distribution of two opinions there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We f…
Online social media such as Twitter are widely used for mining public opinions and sentiments on various issues and topics. The sheer volume of the data generated and the eager adoption by the online-savvy public are helping to raise the profile of online media as a convenient source of news and public opinions on social and political issues as well. Due to the uncontrollable biases in the population who heavily use the media, however, it is often difficult to measure how accurately the online sphere reflects the offline world at large, undermining the usefulness of online media. One way of id…
Social media platforms have emerged as a hub for political and social interactions, and analyzing the polarization of opinions has been gaining attention. In this study, we have proposed a measure to quantify polarization on social networks. The proposed metric, unlike state-of-the-art methods, does not assume a two-opinion case and applies to multiple opinions. We tested our metric on different networks with a multi-opinion scenario and varying degrees of polarization. The scores obtained from the proposed metric were comparable to state-of-the-art methods on binary opinion-based benchmark ne…
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
We explore a new mechanism to explain polarization phenomena in opinion dynamics in which agents evaluate alternative views on the basis of the social feedback obtained on expressing them. High support of the favored opinion in the social environment, is treated as a positive feedback which reinforces the value associated to this opinion. In connected networks of sufficiently high modularity, different groups of agents can form strong convictions of competing opinions. Linking the social feedback process to standard equilibrium concepts we analytically characterize sufficient conditions for th…
Individuals modify their opinions towards a topic based on their social interactions. Opinion evolution models conceptualize the change of opinion as a uni-dimensional continuum, and the effect of influence is built by the group size, the network structures, or the relations among opinions within the group. However, how to model the personal opinion evolution process under the effect of the online social influence as a function remains unclear. Here, we show that the uni-dimensional continuous user opinions can be represented by compressed high-dimensional word embeddings, and its evolution ca…
In this paper, we study the evolution of opinions over social networks with bounded confidence in social cliques. Node initial opinions are independently and identically distributed; at each time step, nodes review the average opinions of a randomly selected local clique. The clique averages may represent local group pressures on peers. Then nodes update their opinions under bounded confidence: only when the difference between an agent individual opinion and the corresponding local clique pressure is below a threshold, this agent opinion is updated according to the DeGroot rule as a weighted a…
Social influence is the process by which individuals adapt their opinion, revise their beliefs, or change their behavior as a result of social interactions with other people. In our strongly interconnected society, social influence plays a prominent role in many self-organized phenomena such as herding in cultural markets, the spread of ideas and innovations, and the amplification of fears during epidemics. Yet, the mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation. Here, we report two controlled experiments showing…
There are some shreds of evidence that social opinion polarization leads to the breakup of the relationship, some in the scale of small communities, but others can divide large organizations or even a nation. The legacy methodology to answer the root cause of opinion polarization in the society commonly use random sampling or questionnaire-based approach, which considered expensive in term of time and money. On the contrary, the opportunity to employ big data approach using social media data provides a rich source to investigate several questions, such as: how social opinion polarization forme…
When opinions, behaviors or ideas diffuse within a population, some are invariably stickier than others. The stickier the opinion, behavior or idea, the greater is an individual's inertia to replace it with an alternative. Here we study the effect of stickiness of opinions in a two-opinion model, where individuals change their opinion only after a certain number of consecutive encounters with the alternative opinion. Assuming that one opinion has a fixed stickiness, we investigate how the critical size of the competing opinion required to tip over the entire population varies as a function of …
Bounded confidence models of opinion dynamics have been actively studied in recent years, in particular, opinion formation and extremism propagation along with other aspects of social dynamics. In this work, after an analysis of limitations of the Deffuant-Weisbuch (DW) bounded confidence, relative agreement model, we propose the Mixed model that takes into account two psychological types of individuals. Concord agents (C-agents) are friendly people; they interact in a way that their opinions get closer always. Agents of the other psychological type show partial antagonism in their interaction…
This paper aims to provide a systemic analysis to social opinion dynamics subject to individual biases. As a generalization of the classical DeGroot social interactions, defined by linearly coupled dynamics of peer opinions that evolve over time, biases add to state-dependent edge weights and therefore lead to highly nonlinear network dynamics. Previous studies have dealt with convergence and stability analysis of such systems for a few specific initial node opinions and network structures, and here we focus on how individual biases affect social equilibria and their stabilities. First of all,…
This paper proposes a network model of opinion dynamics based on both the social network structure and network centralities. The conceptual novelty in this model is that the opinion of each individual is weighted by the associated network centrality in characterizing the opinion spread on social networks. Following a degree-centrality-weighted opinion dynamics model, we provide an algorithm to partition nodes of any graph into two and multiple clusters based on opinion disagreements. Furthermore, the partition algorithm is applied to real-world social networks including the Zachary karate club…
Instead of studying the properties of social relationship from an objective view, in this paper, we focus on individuals' subjective and asymmetric opinions on their interrelationships. Inspired by the theories from sociolinguistics, we investigate two individuals' opinions on their interrelationship with their interactive language features. Eliminating the difference of personal language style, we clarify that the asymmetry of interactive language feature values can indicate individuals' asymmetric opinions on their interrelationship. We also discuss how the degree of opinions' asymmetry is r…
The heterogeneity of the influence processes is an important feature of social systems: how we perceive social influence and how we influence other individuals is heavily influenced by our opinion and non-opinion attributes. The latter include demographic, cultural, and structural (how we are embedded in social networks) characteristics. Furthermore, the results of the influence processes may also depend on how similar the interacting individuals are in terms of their features. This paper addresses this issue and elaborates on an agent-based model that is sensitive to the individual characteri…
Opinions are an integral part of how we perceive the world and each other. They shape collective action, playing a role in democratic processes, the evolution of norms, and cultural change. For decades, researchers in the social and natural sciences have tried to describe how shifting individual perspectives and social exchange lead to archetypal states of public opinion like consensus and polarization. Here we review some of the many contributions to the field, focusing both on idealized models of opinion dynamics, and attempts at validating them with observational data and controlled sociolo…
Though current researches often study the properties of online social relationship from an objective view, we also need to understand individuals' subjective opinions on their interrelationships in social computing studies. Inspired by the theories from sociolinguistics, the latest work indicates that interactive language can reveal individuals' asymmetric opinions on their interrelationship. In this work, in order to explain the opinions' asymmetry on interrelationship with more latent factors, we extend the investigation from single relationship to the structural context in online social net…
We propose a new Ising-PageRank model of opinion formation on a social network by introducing an Ising- or spin-like structure of the corresponding Google matrix. Each elector or node of the network has two components corresponding to a red or blue opinion in the society. Also each elector propagates either the red or the blue opinion on the network so that the links between electors are described by two by two matrices favoring one or the other of the two opinions. An elector votes for red or blue depending on the dominance of its red or blue PageRank vector components. We determine the depen…
In this paper, we present an empirical study of the opinion dynamics of a large-scale sample of online social network users. We estimate opinions of users as continuous scalars based on their subscriptions to information sources and analyze how friendship connections affect the dynamics of these estimations. Distinguishing between positive (toward opinions of friends) and negative (away from opinions of friends) opinion shifts, we find that the existence and magnitude of opinion shifts are positively related (largely through a linear form or an inverted U-shaped form) to the degree of divergen…
In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the 2D Voter Model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. In this toy market model, social temperature represents nervousness of agents towards market imbalances representing speculative risk. We use the knowledge about the discontinuous Generalized Voter Model phase transition to determine critical fixed points. The system exhibits meta…
