Opinion Dynamics and Sociophysics

受 Ising 模型启发的社会物理学模型

Sociophysics models inspired by the Ising model

本综述探讨了 Ising 及类 Ising 模型在社会物理系统中的应用，展示了其在观点动力学、金融市场等领域的集体行为特征，并强调了演化动力学规则的作用及未来研究方向。

Sociophysics of Intractable Conflicts: Three-Group Dynamics

We extend a sociophysics model of two-group conflict dynamics to three groups. The model with attractors and chaos is proposed as a tool for exploring and managing intractable conflicts. It can be used to generate scenarios of trajectories and outcomes. We use mean-field theory for long-range interactions to study the time dependence of the three grousp' mean attitudes. We find that at some intermediate temperatures the group mean attitudes oscillate in time. Independent of initial conditions, trajectories converge overtime to an attractor in the three-dimensional space of mean attitudes. We u…

Consensus Emerging from the Bottom-up: the Role of Cognitive Variables in Opinion Dynamics

The study of opinions $-$ e.g., their formation and change, and their effects on our society $-$ by means of theoretical and numerical models has been one of the main goals of sociophysics until now, but it is one of the defining topics addressed by social psychology and complexity science. Despite the flourishing of different models and theories, several key questions still remain unanswered. The aim of this paper is to provide a cognitively grounded computational model of opinions in which they are described as mental representations and defined in terms of distinctive mental features. We al…

Opinion Dynamics and Collective Decisions

We expect that democracy enables us to utilize collective intelligence such that our collective decisions build and enhance social welfare, and such that we accept their distributive and normative consequences. Collective decisions are produced by voting procedures which aggregate individual preferences and judgments. Before and after, individual preferences and judgments change as their underlying attitudes, values, and opinions change through discussion and deliberation. In large groups, these dynamics naturally go beyond the scope of the individual and consequently might show unexpected sel…

Extremism definitions in opinion dynamics models

There are several opinion dynamics models where extremism is defined as part of their characteristics. However, the way extremism is implemented in each model does not correspond to equivalent definitions. While some models focus on one aspect of the problem, others focus on different characteristics. This paper shows how each model only captures part of the problem and how Bayesian inspired opinion models can help put those differences in perspective. That discussion suggests new ways to introduce variables that can represent the problem of extremism better than we do today. Keywords: Extremi…

Formation of lightning in terms of opinion dynamics in three dimension

Formation of a lightning within a cloud, between clouds and towards the earth is studied as an application of sociophysics. The three dimensional society is sky or cloud, which has members as electrically charged clouds (in sky) or patches (in cloud). Members interact with the neighboring ones and all are convinced to average their charges (opinion). Yet, big external drives (mass media) as winds and turbulences may load new charges or may force the present ones to accumulate temporally at a site. For a lightning towards the earth, similarly charged clouds in sky (patches carrying big charges …

Sznajd model and its applications

In 2000 we proposed a sociophysics model of opinion formation, which was based on trade union maxim "United we Stand, Divided we Fall" (USDF) and latter due to Dietrich Stauffer became known as the Sznajd model (SM). The main difference between SM compared to voter or Ising-type models is that information flows outward. In this paper we review the modifications and applications of SM that have been proposed in the literature.

Opinion dynamics involving contrarian and independence behaviors based on the Sznajd model with two-two and three-one agent interactions

We investigate the opinion evolution of outflow dynamics based on the Sznajd model on a complete graph involving contrarian and independence behaviors. We consider a group of four spins representing the social agents with the following scenarios: (1) scenario two-two with contrarian agents or independence agents and (2) scenario three-one with contrarian or independence agents. All of them undergo a second-order phase transition according to our simulation. The critical point decreases exponentially as $λ$ and $f$ increases, where $λ$ and $f$ are contrarian and flexibility factors, respectivel…

From 2000 Bush-Gore to 2006 Italian elections: Voting at fifty-fifty and the Contrarian Effect

A sociophysical model for opinion dynamics is shown to embody a series of recent western hung national votes all set at the unexpected and very improbable edge of a fifty-fifty score. It started with the Bush-Gore 2000 American presidential election, followed by the 2002 Stoiber-Schrőder, then the 2005 Schrőder-Merkel German elections, and finally the 2006 Prodi-Berlusconi Italian elections. In each case, the country was facing drastic choices, the running competing parties were advocating very different programs and millions of voters were involved. Moreover, polls were given a substantial ma…

D-MODD：从在线数据推导出的意见动态扩散模型

D-MODD: A Diffusion Model of Opinion Dynamics Derived from Online Data

D-MODD 模型通过实证方法推导出意见动态的连续时间随机模型，揭示了极化话题中意见变化的马尔可夫特性。

Continuous Opinion Dynamics under Bounded Confidence: A Survey

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…

大规模外生事件下的意见动力学

Opinion dynamics under large-scale exogenous events

本研究提出通用随机过程框架，分析大规模外生冲击对意见形成的影响，揭示冲击对达成共识的利弊条件及新型多峰状态。

网络上涉及非从众行为的非线性 $q$-voter 模型

Nonlinear $q$-voter model involving nonconformity on networks

研究在完全图与无标度网络上构建含反从众、独立及怀疑参数 $s$ 的非线性 $q$-voter 模型，揭示其相变条件并证明二者均属平均场 Ising 普适类。

Benefits of Diversity, Communication Costs, and Public Opinion Dynamics

We study the dynamics of public opinion in a model in which agents change their opinions as a result of random binary encounters if the opinion difference is below their individual thresholds that evolve over time. We ground these thresholds in a simple individual cost-benefit analysis with linear benefits of diversity and quadratic communication costs. We clarify and deepen the results of earlier continuous-opinion dynamics models (Deffuant et al., Adv Complex Systems 2000; Weisbuch et al., Complexity 2002) and establish several new results regarding the patterns of opinions in the asymptotic…

Transfer in multi-theme opinion dynamics of Deffuant et al

Monte Carlo simulations mix the opinion dynamics of Deffuant et al with the cultural transfer model of Axelrod, using ten discrete possible opinions on ten different themes. As Jacobmeier's simulations of the pure Deffuant case, people preferably agree on nearly all or nearly no theme.

Continuous Opinions and Discrete Actions in Opinion Dynamics Problems

A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction between neighbors and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.

The noisy Hegselmann-Krause model for opinion dynamics

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause's rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the…

Phase transition in Nowak-Sznajd opinion dynamics

The Nowak modification of the Sznajd opinion dynamics model on the square lattice assumes that with probabilities beta and gamma the opinions flip due to mass-media advertising from down to up, and vice versa. Besides, with probability alpha the Sznajd rule applies that a neighbour pair agreeing in its two opinions convinces all its six neighbours of that opinion. Our Monte Carlo simulations and mean-field theory find sharp phase transitions in the parameter space.

Person-to-person opinion dynamics: an empirical study using an online game

A model needs to make verifiable predictions to have any scientific value. In opinion dynamics, the study of how individuals exchange opinions with one another, there are many theoretical models which attempt to model opinion exchange, one of which is the Martins model, which differs from other models by using a parameter that is easier to control for in an experiment. In this paper, we have designed an experiment to verify the Martins model and contribute to the experimental design in opinion dynamic with our novel method.

Opinion dynamics: Public and private

We study here the dynamics of opinion formation in a society where we take into account of the internally held beliefs and externally expressed opinions of the individuals, which are not necessarily the same at all times. While these two components can influence one another, their difference, both in dynamics and in the steady state, poses interesting scenarios in terms of the transition to consensus in the society and characterizations of such consensus. Here we study this public and private opinion dynamics and the critical behavior of the consensus forming transitions, using a kinetic excha…

耦合内隐与外显观点的动力学

Dynamics of coupled implicit and explicit opinions

本文基于双重态度理论提出内隐与外显观点协同演化模型，分析对抗讨论中偏见程度对观点共识、外显顺从及内隐极化的影响，并通过数值模拟验证接受与顺从现象。

A stabilization theorem for dynamics of continuous opinions

A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann-Krause and Weisbuch-Deffuant). The analysis detects self-confidence as a driving force of stabilization.

Opinion dynamics and consensus formation in a Deffuant model with extremists and moderates

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 …

Spontaneous reorientations in a model of opinion dynamics with anticonformists

In this paper we investigate a model (based on the idea of the outflow dynamics), in which only conformity and anticonformity can lead to the opinion change. We show that for low level of aniconformity the consensus is still reachable but spontaneous reorientations between two types of consensus ('all say yes' or 'all say now') appear.

Rise of the centrist: from binary to continuous opinion dynamics

We propose a model that extends the binary ``united we stand, divided we fall'' opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are …

Continuous Opinion Dynamics: Insights through Interactive Markov Chains

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 relative approach to opinion formation

Formal models of opinion formation commonly represent an individual's opinion by a value on a fixed opinion interval. We propose an alternative modeling method wherein interpretation is only provided to the relative positions of opinions vis-à-vis each other. This method is then considered in a similar setting as the discrete-time Altafini model (an extension of the well-known DeGroot model), but with more general influence weights. Even in a linear framework, the model can describe, in the long run, polarization, dynamics with a periodic pattern, and (modulus) consensus formation. In addition…

Finite-size effects on the convergence time in continuous-opinion dynamics

We study finite-size effects on the convergence time in a continuous-opinion dynamics model. In the model, each individual's opinion is represented by a real number on a finite interval, e.g., $[0,1]$, and a uniformly randomly chosen individual updates its opinion by partially mimicking the opinion of a uniformly randomly chosen neighbor. We numerically find that the characteristic time to the convergence increases as the system size increases according to a particular functional form in the case of lattice networks. In contrast, unless the individuals perfectly copy the opinion of their neigh…

Continuous opinion dynamics of multidimensional allocation problems under bounded confidence: More dimensions lead to better chances for consensus

We study multidimensional continuous opinion dynamics, where opinions are nonnegative vectors which components sum up to one. Examples of such opinions are budgets or other allocation vectors which display a distribution of a fixed amount of ressource to n projects. We use the opinion dynamics models of Deffuant-Weisbuch and Hegselmann-Krause, which both extend naturally to more dimensional opinions. They both rely on bounded confidence of the agents and differ in their communication regime. We show detailed simulation results regarding $n=2,...,8$ and the bound of confidence $\eps$. Number, l…

An energy-based interaction model for population opinion dynamics with topic coupling

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…

Truth seekers in opinion dynamics models

We modify the model of Deffuant et al. to distinguish true opinion among others in the fashion of Hegselmann and Krause <http://jasss.soc.surrey.ac.uk/9/3/10.html>. The basic features of both models modified to account for truth seekers are qualitatively the same.

Socioeconophysics: Opinion Dynamics for number of transactions and price, a trader based model

Involving effects of media, opinion leader and other agents on the opinion of individuals of market society, a trader based model is developed and utilized to simulate price via supply and demand. Pronounced effects are considered with several weights and some personal differences between traders are taken into account. Resulting time series and probabilty distribution function involving a power law for price come out similar to the real ones.

算法偏见下社交网络中的观点形成：动力学与偏见失衡

Opinion formation on social networks with algorithmic bias: Dynamics and bias imbalance

本文构建含算法偏见、社区结构、噪声及群体交互的网络观点演化模型，揭示偏见失衡如何决定最终舆论状态、相变及收敛时间。

Max-Plus Opinion Dynamics With Temporal Confidence

Often in the setting of human-based interactions, the existence of a temporal hierarchy of information plays an important role in diffusion and opinion dynamics within communities. For example at the individual agent level, more recently acquired information may exert greater influence during decision-making processes. To facilitate further exploration of this effect, we introduce an efficient method for modelling temporally asynchronous opinion updates, where the timing of updates depends on the timing of incoming opinion states received from neighbours. The framework enables the introduction…

Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation

We propose and investigate different kinetic models for opinion formation, when the opinion formation process depends on an additional independent variable, e.g. a leadership or a spatial variable. More specifically, we consider:(i) opinion dynamics under the effect of opinion leadership, where each individual is characterised not only by its opinion, but also by another independent variable which quantifies leadership qualities; (ii) opinion dynamics modelling political segregation in the `The Big Sort', a phenomenon that US citizens increasingly prefer to live in neighbourhoods with politica…

有偏动态网络上的观点动力学：超越罕见观点更新

Opinion dynamics on biased dynamical networks: beyond rare opinion updating

针对观点更新与网络演化时间尺度任意的情形，本文提出基于决定系数和一维稳定流形的解析近似，推导固定概率与固定时间，并揭示群体内偏见下从众反而抑制多数观点主导的反直觉规律。

环形意见空间对意见双极化的影响

The effect of a toroidal opinion space on opinion bi-polarisation

本文研究了环形意见空间对意见双极化的影响，发现其在稳态下能形成更多群体，并对扩展更敏感。

Dynamical affinity in opinion dynamics modelling

We here propose a model to simulate the process of opinion formation, which accounts for the mutual affinity between interacting agents. Opinion and affinity evolve self-consistently, manifesting a highly non trivial interplay. A continuous transition is found between single and multiple opinion states. Fractal dimension and signature of critical behaviour are also reported. A rich phenomenology is presented and discussed with reference to corresponding psychological implications.

Opinion Dynamics Models with Memory in Coopetitive Social Networks: Analysis, Application and Simulation

In some social networks, the opinion forming is based on its own and neighbors' (initial) opinions, whereas the evolution of the individual opinions is also influenced by the individual's past opinions in the real world. Unlike existing social network models, in this paper, a novel model of opinion dynamics is proposed, which describes the evolution of the individuals' opinions not only depends on its own and neighbors' current opinions, but also depends on past opinions. Memory and memoryless communication rules are simultaneously established for the proposed opinion dynamics model. Sufficien…

切换网络上的意见动力学

Opinion dynamics on switching networks

研究有向多层网络上的意见动力学，其中邻接矩阵随不同网络层交互频率而时变，旨在刻画不同层激活频率对意见动力学过程收敛性的影响。

Opinion Particles: Classical Physics and Opinion Dynamics

A model for Opinion Particles, based on Bayesian-inspired models of Opinion Dynamics such as the CODA model is presented. By extending the discrete time characteristic of those models to continuous time, a theory for the movement of opinion particles is obtained, based only on inference ideas. This will allow inertia to be obtained as a consequence of an extended CODA model. For the general case, we will see that the likelihoods are associated with variables such as velocity and acceleration of the particles. Newtonian forces are easily defined and the relationship between a force and the equi…

Opinion dynamics of random-walking agents on a lattice

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…

Consensus, polarisation and coexistence in a continuous opinion dynamics model with quenched disorder

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…

Opinion Dynamics on Complex Networks

Social media has emerged as a significant source of information for people. As agents interact with each other through social media platforms, they create numerous complex social networks. Within these networks, information spread among agents and their opinions may be altered by their neighbors' influence. This paper explores opinion dynamics on social networks, which are influenced by complex network structure, confirmation bias, and specific issues discussed. We propose a novel model based on previous models to simulate how public opinion evolves from consensus to radicalization and to pola…

Opinion Dynamics Theory for Analysis of Consensus Formation and Division of Opinion on the Internet

The massive amount of text data on the web has facilitated research on the quantitative analysis of public opinion, which could not be visualized earlier. In this paper, we propose a new opinion dynamics theory. This theory that is intended to explain agreement formation and opinion breakup division in opinion exchanges on social media such as Twitter. With the popularization of the public network, we have become able to communicate with instantaneity and interactivity beyond the temporal and spatial constraints.Research on quantitatively analyzing the distribution of opinion on public opinion…

The dynamics of opinion expression

Modelling efforts in opinion dynamics have to a large extent ignored that opinion exchange between individuals can also have an effect on how willing they are to express their opinion publicly. Here, we introduce a model of public opinion expression. Two groups of agents with different opinion on an issue interact with each other, changing the willingness to express their opinion according to whether they perceive themselves as part of the majority or minority opinion. We formulate the model as a multi-group majority game and investigate the Nash equilibria. We also provide a dynamical systems…

Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions

In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties -friendships and enmities- evolve seeking for social balance, taking into account how similar agents' opinions are. We consider both the case where opinions have one and two dimensions. We find that our dynamics produces the segregation of agents into two cliques, with the opinions of agents in one clique differing from those in the other. Depending on the level of…

Learning and Forecasting Opinion Dynamics in Social Networks

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…

Opinion Dynamics and Influencing on Random Geometric Graphs

We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evol…

从听到的意见到 lived 的意见：利用 grounded LLM 代理在经济环境中模拟意见动态

From Heard to Lived Opinions: Simulating Opinion Dynamics with Grounded LLM Agents in Economic Environments

本文提出一种基于经济环境的LLM代理框架，通过模拟个体经济经历影响意见动态，揭示个体与群体意见变化的机制及经济因素对极化的影响。

基于智能体模型的意见与社会动态协同演化网络

Co-evolving networks for opinion and social dynamics in agent-based models

本研究提出随机智能体模型，协同演化意见与社会动态，分析回音室和共识机制，并应用于综合社会调查数据，验证其捕捉社会联系与意见随时间协同演化的能力。

Opinion groups formation and dynamics : structures that last from non lasting entities

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…

Interplay between media and social influence in the collective behavior of opinion dynamics

Messages conveyed by media act as a major drive in shaping attitudes and inducing opinion shift. On the other hand, individuals are strongly affected by peer pressure while forming their own judgment. We solve a general model of opinion dynamics where individuals either hold one of two alternative opinions or are undecided and interact pairwise while exposed to an external influence. As media pressure increases, the system moves from pluralism to global consensus; four distinct classes of collective behavior emerge, crucially depending on the outcome of direct interactions among individuals ho…

Balancer effects in opinion dynamics

We introduce a novel type of contrarian agent, the balancer, to Galam model of opinion dynamics, in order to account for the existence of social skepticism over one-sidedness. We find that the inclusion of balancers, along with majoritarian floaters and single-sided inflexibles, brings about the emergence of a critical point on parametric plane of the dynamical system. Around the critical point, three distinct phases of opinion dynamics separated by discontinuous changes are found.