It is known that individual opinions on different policy issues often align to a dominant ideological dimension (e.g. "left" vs. "right") and become increasingly polarized. We provide an agent-based model that reproduces these two stylized facts as emergent properties of an opinion dynamics in a multi-dimensional space of continuous opinions. The mechanisms for the change of agents' opinions in this multi-dimensional space are derived from cognitive dissonance theory and structural balance theory. We test assumptions from proximity voting and from directional voting regarding their ability to reproduce the expected emerging properties. We further study how the emotional involvement of agents, i.e. their individual resistance to change opinions, impacts the dynamics. We identify two regimes for the global and the individual alignment of opinions. If the affective involvement is high and shows a large variance across agents, this fosters the emergence of a dominant ideological dimension. Agents align their opinions along this dimension in opposite directions, i.e. create a state of polarization.
We propose an agent-based model of collective opinion formation to study the wisdom of crowds under social influence. The opinion of an agent is a continuous positive value, denoting its subjective answer to a factual question. The wisdom of crowds states that the average of all opinions is close to the truth, i.e. the correct answer. But if agents have the chance to adjust their opinion in response to the opinions of others, this effect can be destroyed. Our model investigates this scenario by evaluating two competing effects: (i) agents tend to keep their own opinion (individual conviction $…
Traditional models of opinion dynamics provide a simple approach to understanding human behavior in basic social scenarios. However, when it comes to issues such as polarization and extremism, we require a more nuanced understanding of human biases and cognitive tendencies. In this paper, we propose an approach to modeling opinion dynamics by integrating mental models and assumptions of individuals agents using Bayesian-inspired methods. By exploring the relationship between human rationality and Bayesian theory, we demonstrate the efficacy of these methods in describing how opinions evolve. O…
We provide an agent-based model to explain the emergence of collective opinions not based on feedback between different opinions, but based on emotional interactions between agents. The driving variable is the emotional state of agents, characterized by their valence and their arousal. Both determine their emotional expression, from which collective emotional information is generated. This information feeds back on the dynamics of emotional states and of individual opinions in a non-linear manner. We derive the critical conditions for emotional interactions to obtain either consensus or polari…
We consider a recent model in which agents hold opinions about each other and influence each other's opinions during random pair interactions. When the opinions are initially close, on the short term, all the opinions tend to increase over time. On the contrary, when the opinions are initially very unequal, the opinions about agents of high status increase, but the opinions about agents of low status tend to stagnate without gossip and to decrease with gossip. We derive a moment approximation of the average opinion changes that explains these observations.
Within the framework of a simple model for social influence, the Taylor model, we analytically investigate the role of stubborn agents in the overall opinion dynamics of networked systems. Similar to zealots, stubborn agents are biased towards a certain opinion and have a major effect on the collective opinion formation process. Based on a modified version of the network Laplacian we derive quantities capturing the transient dynamics of the system and the emerging stationary opinion states. In the case of a single stubborn agent we characterize his/her ability to coherently change a prevailing…
A model for the joint evolution of opinions and how much the agents trust each other is presented. The model is built using the framework of the Continuous Opinions and Discrete Actions (CODA) model. Instead of a fixed probability that the other agents will decide in the favor of the best choice, each agent considers that other agents might be one one of two types: trustworthy or useless. Trustworthy agents are considered more likely to be right than wrong, while the opposite holds for useless ones. Together with the opinion about the discussed issue, each agent also updates that probability f…
We study an endogenous opinion (or, belief) dynamics model where we endogenize the social network that models the link (`trust') weights between agents. Our network adjustment mechanism is simple: an agent increases her weight for another agent if that agent has been close to truth (whence, our adjustment criterion is `past performance'). Moreover, we consider multiply biased agents that do not learn in a fully rational manner but are subject to persuasion bias - they learn in a DeGroot manner, via a simple `rule of thumb' - and that have biased initial beliefs. In addition, we also study this…
This paper introduces a Markov chain approach that allows a rigorous analysis of agent based opinion dynamics as well as other related agent based models (ABM). By viewing the ABM dynamics as a micro description of the process, we show how the corresponding macro description is obtained by a projection construction. Then, well known conditions for lumpability make it possible to establish the cases where the macro model is still Markov. In this case we obtain a complete picture of the dynamics including the transient stage, the most interesting phase in applications. For such a purpose a cruci…
It has been observed people tend to have opinions that are far more internally consistent than it would be reasonable to expect. Here, we study how that observation might emerge from changing how agents trust the opinions of their peers in a model for opinion dynamics with multiple issues. A previous Bayesian inspired opinion model for continuous opinions is extended to include multiple issues. In the original model, agents tended to trust less opinions that were too different from their own. We investigate the properties of the extended model in its natural form. And we also introduce the pos…
The effect of undecided agents is studied within populations in an opinion-forming dynamic, varying the number of undecided agents for different proportions of populations in a complete opinion-exchange network. The result is that the dynamic depends on the number of undecided agents, with 10\% of the undecided population potentially affecting the change in consensus and then becoming linear with a negative slope.
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…
Agent-based models are versatile tools for studying how societal opinion change, including political polarization and cultural diffusion, emerges from individual behavior. This study expands agents' psychological realism using empirically-motivated rules governing interpersonal influence, commitment to previous beliefs, and conformity in social contexts. Computational experiments establish that these extensions produce three novel results: (a) sustained strong diversity of opinions within the population, (b) opinion subcultures, and (c) pluralistic ignorance. These phenomena arise from a combi…
Opinion dynamics of random-walking agents on finite two-dimensional lattices is studied. In the model, the opinion is continuous, and both the lattice and the opinion can be either periodic or non-periodic. At each time step, all agents move randomly on the lattice, and update their opinions based on those of neighbors with whom the differences of opinions are not greater than a given threshold. Due to the effect of repeated averaging, opinions first converge locally, and eventually reach steady states. Like other models with bounded confidence, steady states in general are those with one or m…
We study opinion dynamics in a population of interacting adaptive agents voting on a set of complex multidimensional issues. We consider agents which can classify issues into for or against. The agents arrive at the opinions about each issue in question using an adaptive algorithm. Adaptation comes from learning and the information for the learning process comes from interacting with other neighboring agents and trying to change the internal state in order to concur with their opinions. The change in the internal state is driven by the information contained in the issue and in the opinion of t…
We study a stochastic model for the coevolution of a process of opinion formation in a population of agents and the network which underlies their interaction. Interaction links can break when agents fail to reach an opinion agreement. The structure of the network and the distribution of opinions over the population evolve towards a state where the population is divided into disconnected communities whose agents share the same opinion. The statistical properties of this final state vary considerably as the model parameters are changed. Community sizes and their internal connectivity are the qua…
We study the joint evolution of worldviews by proposing a model of opinion dynamics, which is inspired in notions from evolutionary ecology. Agents update their opinion on a specific issue based on their propensity to change -- asserted by the social neighbours -- weighted by their mutual similarity on other issues. Agents are, therefore, more influenced by neighbours with similar worldviews (set of opinions on various issues), resulting in a complex co-evolution of each opinion. Simulations show that the worldview evolution exhibits events of intermittent polarization when the social network …
There are numerous examples of societies with extremely stable mix of contrasting opinions. We argue that this stability is a result of an interplay between society network topology adjustment and opinion changing processes. To support this position we present a computer model of opinion formation based on some novel assumptions, designed to bring the model closer to social reality. In our model, the agents, in addition to changing their opinions due to influence of the rest of society and external propaganda, have the ability to modify their social network, forming links with agents sharing t…
Processes of individual attitude formation and their macroscopic consequences have become an intriguing research topic, and agent-based models of opinion formation have been proposed to understand this phenomenon. This study conducted an agent-based simulation and examined the role of mass media in a noisy opinion formation process, where opinion heterogeneity is preserved by a weak intensity of assimilation and errors accompanying opinion modifications. In a computational model, agents conformed to their neighbours' opinions in social networks. In addition, each agent tended to be influenced …
Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines as physics, mathematics, computer science, social psychology and philosophy. Agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to eac…
This article contributes in four ways to the research on time-discrete continuous opinion dynamics with compromising agents. First, communication regimes are introduced as an elementary concept of opinion dynamic models. Second, we develop a model that covers two major models of continuous opinion dynamics, i.e. the basic model of Deffuant and Weisbuch as well as the model of Krause and Hegselmann. To combine these models, which handle different numbers of communicating agents, we convert the convergence parameter of Deffuant and Weisbuch into a parameter called self-support. Third, we present…
We propose a nonlinear voter model to study the emergence of global consensus in opinion dynamics. In our model, agent $i$ agrees with one of binary opinions with the probability that is a power function of the number of agents holding this opinion among agent $i$ and its nearest neighbors, where an adjustable parameter $α$ controls the effect of herd behavior on consensus. We find that there exists an optimal value of $α$ leading to the fastest consensus for lattices, random graphs, small-world networks and scale-free networks. Qualitative insights are obtained by examining the spatiotemporal…
We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time it interacts with another agent who has a different opinion. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short, i.e. the system self-organizes into a critic…
We propose and study a stochastic binary opinion model where agents in a group are considered to hold an opinion of 0 or 1 at each moment. An agent in the group updates his/her opinion based on the group's opinion configuration and his/her \emph{personality}. Considering the number of agents with opinion 1 as a continuous time Markov process, we analyze the long-term probabilities for large population size in relation to the personalities of the group. In particular, we focus on the question of ``balance'' where both opinions are present in nearly equal numbers as opposed to ``dominance'' wher…
In this paper we study the impact of active participation -- or deliberately seeking out other agents with an aim to convince them -- on the dynamics of consensus formation. For this purpose, we propose an adaptive network model in which two processes shape opinion dynamics at interwoven time-scales: (i) agents adapt their opinions subject to influence from social network neighbours who hold opinions within a tolerance interval $δ$ and (ii) agents rewire network connections with an aim to maximize their own influence on overall system opinion. We study this system in both an endogenous setting…
We consider the problem of optimizing the placement of stubborn agents in a social network in order to maximally influence the population. We assume the network contains stubborn users whose opinions do not change, and non-stubborn users who can be persuaded. We further assume the opinions in the network are in an equilibrium that is common to many opinion dynamics models, including the well-known DeGroot model. We develop a discrete optimization formulation for the problem of maximally shifting the equilibrium opinions in a network by targeting users with stubborn agents. The opinion objectiv…
We study dynamics of opinion formation in a network of coupled agents. As the network evolves to a steady state, opinions of agents within the same community converge faster than those of other agents. This framework allows us to study how network topology and network flow, which mediates the transfer of opinions between agents, both affect the formation of communities. In traditional models of opinion dynamics, agents are coupled via conservative flows, which result in one-to-one opinion transfer. However, social interactions are often non-conservative, resulting in one-to-many transfer of op…
We define an opinion formation model of agents in a 1d ring, where the opinion of an agent evolves due to its interactions with close neighbors and due to its either positive or negative attitude toward the overall mood of all the other agents. While the dynamics of the agent's opinion is described with an appropriate differential equation, from time to time pairs of agents are allowed to change their locations to improve the homogeneity of opinion (or comfort feeling) with respect to their short range environment. In this way the time scale of transaction dynamics and that of environment upda…
The original Hegselmann-Krause (HK) model consists of a set of~$n$ agents that are characterized by their opinion, a number in~$[0, 1]$. Each agent, say agent~$i$, updates its opinion~$x_i$ by taking the average opinion of all its neighbors, the agents whose opinion differs from~$x_i$ by at most~$ε$. There are two types of~HK models: the synchronous~HK model and the asynchronous~HK model. For the synchronous model, all the agents update their opinion simultaneously at each time step, whereas for the asynchronous~HK model, only one agent chosen uniformly at random updates its opinion at each ti…
We present a novel software suite for social network modeling and opinion diffusion processes. Much research on social network science has assumed networks with static topologies. More recently, attention has been turned to networks that evolve. Although software for modeling both the topological evolution of networks and diffusion processes are constantly improving, very little attention has been paid to agent modeling. Our software is designed to be robust, modular, and extensible, providing the ability to model dynamic social network topologies and multidimensional diffusion processes, diff…
The voter model is a simple agent-based model to mimic opinion dynamics in social networks: a randomly chosen agent adopts the opinion of a randomly chosen neighbour. This process is repeated until a consensus emerges. Although the basic voter model is theoretically intriguing, it misses an important feature of real opinion dynamics: it does not distinguish between an agent's publicly expressed opinion and her inner conviction. A person may not feel comfortable declaring her conviction if her social circle appears to hold an opposing view. Here we introduce the Concealed Voter Model where we a…
Opinion formation is a process with strong implications for public policy. In controversial debates with large consequences, the public opinion is often trapped in a fifty-fifty stalemate, jeopardizing broadly accepted political decisions. Emergent effects from millions of private discussions make it hard to understand or influence this kind of opinion dynamics. Here we demonstrate that repulsion from opinions favors fifty-fifty stalemates. We study a voter model where agents can have two opinions or an undecided state in-between. In pairwise discussions, undecided agents can be convinced or r…
The diffusion of opinions in Social Networks is a relevant process for adopting positions and attracting potential voters in political campaigns. Opinion polarization, bias, targeted diffusion, and the radicalization of postures are key elements for understanding voting dynamics. In particular, social bots are a new element that can have a pronounced effect on the formation of opinions during elections by, for instance, creating fake accounts in social networks to manipulate elections. Here we propose a voter model incorporating bots and radical or intolerant individuals in the decision-making…
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,…
We reformulate the agent-based opinion dynamics models of Weisbuch-Deffuant and Hegselmann-Krause as interactive Markov chains. So we switch the scope from a finite number of n agents to a finite number of n opinion classes. Thus, we will look at an infinite population distributed to opinion classes instead of agents with real number opinions. The interactive Markov chains show similar dynamical behavior as the agent-based models: stabilization and clustering. Our framework leads to a discrete bifurcation diagram for each model which gives a good view on the driving forces and the attractive s…
A simple model of opinion formation dynamics in which binary-state agents make up their opinions due to the influence of agents in a local neighborhood is studied using different network topologies. Each agent uses two different strategies, the Sznajd rule with a probability $q$ and the Galam majority rule (without inertia) otherwise; being $q$ a parameter of the system. Initially, the binary-state agents may have opinions (at random) against or in favor about a certain topic. The time evolution of the system is studied using different network topologies, starting from different initial opinio…
The formation of agents' opinions in a social system is the result of an intricate equilibrium among several driving forces. On the one hand, the social pressure exerted by peers favours the emergence of local consensus. On the other hand, the concurrent participation of agents to discussions on different topics induces each agent to develop a coherent set of opinions across all the topics in which he is active. Moreover, the pervasive action of external stimuli, such as mass media, pulls the entire population towards a specific configuration of opinions on different topics. Here we propose a …
We extend simple opinion models to obtain stable but continuously evolving communities. Our scope is to meet a challenge raised by sociologists of generating "structures that last from non lasting entities". We achieve this by introducing two kinds of noise on a standard opinion model. First, agents may interact with other agents even if their opinion difference is large. Second, agents randomly change their opinion at a constant rate. We show that for a large range of control parameters, our model yields stable and fluctuating polarized states, where the composition and mean opinion of the em…
In this work, we study a nonlocal opinion dynamics in a ring of agents with circular opinion in the presence of both attractive and repulsive interactions. We identified three types of consensus in this model, including global consensus, local consensus, and chimera consensus. In global consensus, both local agreement among adjacent agents and global agreement among all agents are achieved. In local consensus, local agreement is satisfied but global agreement fails. There are two domains in chimera consensus, one preserves local agreement and the other breaks the local agreement. The relation …
Agent-based models of opinion dynamics allow one to examine the spread of opinions between entities and to study phenomena such as consensus, polarization, and fragmentation. By studying a model of opinion dynamics on a social network, one can explore the effects of network structure on these phenomena. In social networks, some individuals share their ideas and opinions more frequently than others. These disparities can arise from heterogeneous sociabilities, heterogeneous activity levels, different prevalences to share opinions when engaging in a social-media platform, or something else. To e…
A model of opinion formation on a Small World type topology is studied to observe qualitatively its difference with one is own conviction versus the opinion of others. It is possible to observe that the relation between conviction to copy the agent with whom it interacts and this agent is an undecided agent who leaves decisions to chance becomes outstanding since the probability of undecided agents is greater than 0.1 and is maintained until 0.7 so that in the border regions, it is only a transition towards this predictive.
The Hegselmann-Krause (HK) model allows one to characterize the continuous change of agents' opinions with the bounded confidence threshold $\varepsilon$. To consider the heterogeneity of agents in characteristics, we study the HK model on homogeneous and heterogeneous networks by introducing a kind of smart agent. Different from the averaging rule in opinion update of HK model, smart agents will consider, in updating their opinions, the environmental influence following the fact that an agent's behavior is often coupled with environmental changes. The environment is characterized by a paramet…
