We study a process of opinion formation in a population of agents whose interaction pattern is defined on the basis of randomly distributed groups of three agents, or triplets -in contrast to networks, which are defined on the basis of agent pairs. Results for the time needed to reach full consensus are compared between a triplet-based structure with a given number of triplets and a random network with the same number of triangles. The full-consensus time in the triplet structure is systematically lower than in the network. This discrepancy can be ascribed to differences in the shape of the probability distribution for the number of triplets and triangles per agent in each interaction pattern.
The evolution of opinions in a population of individuals who constantly interact with a common source of user-generated content (i.e. the internet) and are also subject to propaganda is analyzed using computer simulations. The model is based on the bounded confidence approach. In the absence of propaganda, computer simulations show that the online population as a whole is either fragmented, polarized or in perfect harmony on a certain issue or ideology depending on the uncertainty of individuals in accepting opinions not closer to theirs. On applying the model to simulate radicalization, a pro…
Among the different disciplines in the social, behavioral and economic sciences, a fundamental class of problems is related to the prediction of the final state of the presence of individual opinions in a large population. The main aspects investigated in the opinion dynamics are related to the possibility of reaching an agreement and the time needed. In general a consensus model allows to understand if a set of interacting agents can reach a consensus when choosing among several options: political vote, opinions, cultural features are well-known examples of them. Opinion dynamics models then …
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.
Considerable effort using techniques developed in statistical physics has been aimed at numerical simulations of agent-based opinion models and analysis of their results. Such work has elucidated how various rules for interacting agents can give rise to steady state behaviors in the agent populations that vary between consensus and fragmentation. At the macroscopic population level, analysis has been limited due to the lack of an analytically tractable governing macro-equation for the continuous population state. We use the integro-differential equation that governs opinion dynamics for the co…
We introduce a new, and quite general variational model for opinion dynamics based on pairwise interaction potentials and a range of opinion evolution protocols ranging from random interactions to global synchronous flows in the opinion state space. The model supports the concept of topic "coupling", allowing opinions held by individuals to be changed via indirect interaction with others on different subjects. Interaction topology is governed by a graph that determines interactions. Our model, which is really a family of variational models, has, as special cases, many of the previously establi…
Confirmation bias and peer pressure both have substantial impacts on the formation of collective decisions. Nevertheless, few attempts have been made to study how the interplay between these two mechanisms affects public opinion evolution. Here we propose an agent-based model of opinion dynamics which incorporates the conjugate effect of confirmation bias (characterized by the population identity scope and individual stubbornness) and peer pressure (described by a susceptibility threshold). We show that the number of opinion fragments first increases and then decreases to one as population ide…
We consider a general class of three--state models where individuals hold one of two opposite opinions, or are neutral, and exchange opinions in generic pairwise interactions. We show that when opinions spread in a population where a fraction of individuals (zealots) maintain unshakably their opinion, one of four qualitatively distinct kinds of collective dynamics arise, depending on the specific rules governing the social interactions. Unsurprisingly, when their density is high, zealots drive the whole population to consensus on their opinion. For low densities a rich phase diagram emerges: a…
Understanding the social conditions that tend to increase or decrease polarization is important for many reasons. We study a network-structured agent-based model of opinion dynamics, extending a model previously introduced by Flache and Macy (2011), who found that polarization appeared to increased with the introduction of long-range ties but decrease with the number of salient opinions, which they called the population's "cultural complexity." We find the following. First, polarization is strongly path dependent and sensitive to stochastic variation. Second, polarization depends strongly on t…
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…
In this work we consider the presence of contrarian agents in discrete 3-state kinetic exchange opinion models. The contrarians are individuals that adopt the choice opposite to the prevailing choice of their contacts, whatever this choice is. We consider binary as well as three-agent interactions, with stochastic parameters, in a fully-connected population. Our numerical results suggest that the presence of contrarians destroys the absorbing state of the original model, changing the transition to the para-ferromagnetic type. In this case, the consequence for the society is that the three opin…
We generalize a binary majority-vote model on adaptive networks to its plurality-vote counterpart and analyze the time scale to consensus when voters are given more than two options. When opinions are uniformly distributed in the population of voters in the initial state, we find that the time scale to consensus is shorter than the binary vote model from both numerical simulations and mathematical analysis using the master equation for the three-state plurality-vote model. When intervention such as opinion conversion is allowed, as in the case of sudden change of mind of voter for any reason, …
In this work we study a continuous opinion dynamics model considering 3-agent interactions and group pressure. Agents interact in a fully-connected population, and two parameters govern the dynamics: the agents' convictions $λ$, that are homogeneous in the population, and the group pressure $p$. Stochastic parameters also drive the interactions. Our analytical and numerical results indicate that the model undergoes symmetry-breaking transitions at distinct critical points $λ_{c}$ for any value of $p<p^{*}=2/3$, i.e., the transition can be suppressed for sufficiently high group pressure. Such t…
Recent technological changes have increased connectivity between individuals around the world leading to higher frequency interactions between members of communities that would be otherwise distant and disconnected. This paper examines a model of opinion dynamics in interacting communities and studies how increasing interaction frequency affects the ability for communities to retain distinct identities versus falling into consensus or polarized states in which community identity is lost. We also study the effect (if any) of opinion noise related to a tendency for individuals to assert their in…
In this work, we investigate the effect of social media on the process of opinion formation in a human population. This effect is modeled as an external field in the dynamics of the two-dimensional Sznajd model with a probability P for an agent to follow the social media. We investigate the evolution of magnetization, the distribution of decision time and the average relaxation time in the presence of the external field. Our results suggest that the average relaxation time on the lattice of size L follows a power law, where the exponent depends on the probability P. We also show that phase tra…
We study a model of binary decision making when a certain population of agents is initially seeded with two different opinions, `$+$' and `$-$', with fractions $p_1$ and $p_2$ respectively, $p_1+p_2=1$. Individuals can reverse their initial opinion only once based on this information exchange. We study this model on a completely connected network, where any pair of agents can exchange information, and a two-dimensional square lattice with periodic boundary conditions, where information exchange is possible only between the nearest neighbors. We propose a model in which each agent maintains two…
We study the formation of public opinion in a poll process where the current score is open to public. The voters are assumed to vote probabilistically for or against their own preference considering the group opinion collected up to then in the score. The poll-score probability is found to follow the beta distribution in the large polls limit. We demonstrate that various poll results even contradictory to the population preference are possible with non-zero probability density and that such deviations are readily triggered by initial bias. It is mentioned that our poll model can be understood …
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…
A collective opinion formation model under Bayesian updating and confirmation bias
我们提出了一个集体意见形成模型与所谓的确认偏见。确认偏误是一种心理效应，在意见形成的背景下，赞成某个意见的个人容易将新的信息误解为支持个人当前的信念。我们的模型修改了单个个体的贝叶斯决策模型[M.拉宾和J. L. Schrag，Q. J. Econ. 114，37（1999）]的情况下，相互作用的个体的良好混合的人口在没有外部输入。我们数值模拟的模型表明，所有的代理人最终同意的两个意见之一，只有当确认偏差是弱的。否则，随机种群动力学最终会产生不一致的配置（也称为极化），特别是对于大系统尺寸。强烈的确认偏差允许不同部分的个体最终形成不同的不同意配置，以支持相反的意见。
Many studies have explored spreading and diffusion through complex networks. The following study examines a specific case of spreading of opinions in modern society through two spreading schemes, defined as being either through word-of-mouth (WOM), or through online search engines (WEB). We apply both modelling and real experimental results and compare the opinions people adopt through an exposure to their friend`s opinions, as opposed to the opinions they adopt when using a search engine based on the PageRank algorithm. A simulated study shows that when members in a population adopt decisions…
We present an extensive study of the joint effects of heterogeneous social agents and their heterogeneous social links in a bounded confidence opinion dynamics model. The full phase diagram of the model is explored for two different network's topologies and compared to two opposed extreme cases: on one hand heterogeneous agents which constitute a mixed population and on the other, their interactions are modeled by a lattice. The results show that when agents prone to compromising coexist with close minded ones, the steady state of the dynamics shows coexistent phases. In particular, unlike the…
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…
We study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearest-neighbor interactions on a two-dimensional square lattice. Each agent can hold either a positive or a negative opinion orientation, and can have two levels of intensity --moderate and extremist. When two interacting agents have the same orientation become extremists with persuasion probability $p$, while if they have opposite orientations become moderate with compromise probability $q$. These updating rules lead to the formation of same-opinion domains with …
In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a consensus, and how long it takes a consensus to form. This idea has been studied heavily both in physics and in other disciplines, and the answer depends strongly on both the model for opinions and for the network structure on which the opinions evolve. One model that was created to study consensus formation quantitatively is the Deffuant model, in which the opinion distribution of a population evolves via sequentia…
In this work, we investigate a heterogeneous population in the modified Hegselmann-Krause opinion model on complex networks. We introduce the Shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration. Independent of network structures, there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy. Besides, there is the optimal bounded confidence (or subpopulation ratio) of one subpopulation for the smallest number of clusters and the lowest entropy. However, network stru…
Mean-field equations have been developed recently to approximate the dynamics of the Deffuant model of opinion formation. These equations can describe both fully-mixed populations and the case where individuals interact only along edges of a network. In each case, interactions only occur between individuals whose opinions differ by less than a given parameter, called the confidence bound. The size of the confidence bound parameter is known to strongly affect both the dynamics and the number and location of opinion clusters. In this work we carry out a mathematical analysis of the mean-field eq…
We study a variant of the voter model with multiple opinions; individuals can imitate each other and also change their opinion randomly in mutation events. We focus on the case of a population with all-to-all interaction. A noise-driven transition between regimes with multi-modal and unimodal stationary distributions is observed. In the former, the population is mostly in consensus states; in the latter opinions are mixed. We derive an effective death-birth process, describing the dynamics from the perspective of one of the opinions, and use it to analytically compute marginals of the stationa…
Accurate modeling of opinion dynamics has the potential to help us understand polarization and what makes effective political discourse possible or impossible. Here, we use physics-based methods to model the evolution of political opinions within a continuously distributed population. We utilize a network-free system of determining political influence and a local-attraction, distal-repulsion dynamic for reaction to perceived content. Our approach allows for the incorporation of intergroup bias such that messages from trusted in-group sources enjoy greater leeway than out-group ones. We are abl…
We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the majority, while the rest want to make the minority choice. This resembles opinion spreading with "contrarian" agents, but has the game theoretic aspect that agents try to optimize their own situation in ways that are incompatible with the common good. When this fraction is less than 1/2, the population can efficiently self-organize to a state where agents ge…
In this work we tackle a kinetic-like model of opinions dynamics in a networked population endued with a quenched plurality and polarization. Additionally, we consider pairwise interactions that are restrictive, which is modeled with a smooth bounded confidence. Our results show the interesting emergence of nonequilibrium hysteresis and heterogeneity-assisted ordering. Such counterintuitive phenomena are robust to different types of network architectures such as random, small-world and scale-free.
Opinion formation in the population has attracted extensive research interest. Various models have been introduced and studied, including the ones with individuals' free will allowing them to change their opinions. Such models, however, have not taken into account the fact that individuals with different opinions may have different levels of loyalty, and consequently, different probabilities of changing their opinions. In this work, we study on how the non-uniform distribution of the opinion changing probability may affect the final state of opinion distribution. By simulating a few different …
A general model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by every other opinion in the population. It is demonstrated that consensus, polarisation and a spread of moderate opinions are all possible within this model. Using dynamic mean-field theory, we are able to identify the statistical features of the interactions between individuals that give rise to each of the aforementioned emergent phenomena. The nature of the transitions between each of the observed macroscopic states i…
Fixation and Polarization in a Three-Species Opinion Dynamics Model
受文化变化和多样性的动力学的启发，我们在[J. Phys. A 37，8479（2004）]中引入的完全图上推广了三种群约束投票模型。在这个观点动力学模型中，规模为N的人口由“左派”和“右派”组成，他们与“中间派”互动：左派和中间派都可以成为比率为（1+q）/2的左派或比率为（1-q）/2的中间派（右派和中间派也是如此），其中q表示对极端主义（q>0）或中间主义（q<0）的偏见。这一体系承认三个吸引人的固定点和一条“极化”线，沿着这条线，左派和右派的混合物冻结共存。在Fokker-Planck方程的范畴内，通过对种群遗传学模型的映射，计算了在每个吸收态结束的固定概率和这些事件的平均时间。因此，我们显示，特别是在弱的偏见和大的人口规模的限制时，|q| ~1/N和N>>1，波动如何改变平均场的预测：极化是可能的，当q>0，但总是有一个有限的概率达到共识，相反的情况下，当q<0。我们的研究结果证实了随机模拟。
