Dietrich Stauffer
Individuals have opinions but can change them under the influence of others. The recent models of Sznajd (missionaries), of Deffuant et al. (negotiators), and of Krause and Hegselmann (opportunists) are reviewed here, while the voter and Ising models, Galam's majority rule and the Axelrod multicultural model were dealt with by other lecturers at this 8th Granada Seminar.
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No abstract given. Contents: I. Definition and Introduction II. Schelling Model III. Opinion Dynamics IV. Languages, Hierarchies and Football V. Future Directions
A two state model for opinion forming, which has proven heuristic power, is reviewed with a novel emphasis on the existence or absence of a threshold for the dynamics. Monitored by repeated small groups discussions floater agents update their opinion according to a local majority rule. A threshold makes the initial supports to flow towards eitheir one of two opposite attractors with only one single opinion. While odd sizes yield a threshold at fifty percent even sizes, which allow the inclusion of doubt at an opinion tie, produces a threshold shift toward either 0 or 1 giving rise to minority …
Universality of opinions disappearing in sociophysical models of opinion dynamics: From initial multitude of opinions to ultimate consensus
本文通过 voter、Sznajd 和 Latané 三种舆论模型模拟发现，即使初始观点极度分散，系统最终也几乎总能达成单一共识，但不同模型的观点消减动力学和共识时间随系统规模的增长方式存在显著差异。
In this work we consider the influence of mass media in the dynamics of the two-dimensional Sznajd model. This influence acts as an external field, and it is introduced in the model by means of a probability $p$ of the agents to follow the media opinion. We performed Monte Carlo simulations on square lattices with different sizes, and our numerical results suggest a change on the critical behavior of the model, with the absence of the usual phase transition for $p>\sim 0.18$. Another effect of the probability $p$ is to decrease the average relaxation times $τ$, that are log-normally distribute…
Most of the opinion dynamics models in sociophysics have their historic origin in studies two-dimensional magnetization phenomena. This metaphor has proven quite useful, as it allowed to use well known techniques, relating individual behaviours of single spins and their interactions, to large scale properties, such as magnetization or magnetic domains creation. These physical properties were then ``mapped'' to social concepts: spin orientation to a person's views on a specific issue, magnetization to global opinion on the issue, etc. During the past 20 years, the models were significantly expa…
Consensus formation and difference of opinion have long been the subject of research. However, relevant laws and systems within society are being updated to reflect the changes in information networks. Online environment has come to fulfill a major role as a real and concrete place of opposing opinions and consensus formation. In the future, quantitative findings on consensus formation, and findings on relevant trends, must be summarized, and quantitative research related to trends likely to give rise to social and economic risk is required. Thus, the potential for comparing research related t…
Using a bit-string model similar to biological simulations, the competition between different languages is simulated both without and with spatial structure. We compare our agent-based work with differential equations and the competing bit-string model of Kosmidis et al.
The model of Bonabeau et al explains social hierarchies as random: People keep a memory of recent fights, and winners have a higher probability to win again. The question of phase transition and the generalization from square lattices to networks is reviewed here.
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。
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…
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…
In most sociophysical simulations on public opinion, only two opinions are allowed: Pro and Contra. However, in all political elections many people do not vote. Here we analyse two models of dynamics of public opinion, taking into account Indifferent voters: {\it i)} the Sznajd model with symmetry Pro-Contra, {\it ii)} the outflow one move voter model, where Contra's are converted to Indifferent by their Pro neighbours. Our results on the Sznajd model are in an overall agreement with the results of the mean field approach and with those known from the initial model formulation. The simulation …
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…
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 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 …
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.
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…
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: 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。
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…
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。
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。
In this work we study a modified version of the two-dimensional Sznajd sociophysics model. In particular, we consider the effects of agents' reputations in the persuasion rules. In other words, a high-reputation group with a common opinion may convince their neighbors with probability $p$, which induces an increase of the group's reputation. On the other hand, there is always a probability $q=1-p$ of the neighbors to keep their opinions, which induces a decrease of the group's reputation. These rules describe a competition between groups with high reputation and hesitant agents, which makes th…
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.
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 …
We propose a discrete model for how opinion about a given phenomenon, about which various groups of a population have different degrees of enthusiasm, such as fanaticism and extreme social and political positions, including terrorism, may spread. The model, in a certain limit, is the discrete analogue of a deterministic continuum model suggested by others. We carry out extensive computer simulation of the model by utilizing it on lattices with infinite- or short-range interactions, and on (directed) Barabasi-Albert scale-free networks. Several interesting features of the model are demonstrated…
The paper treats opinion dynamics of an unequal distribution as the initial opinion distribution. Simulated is the Deffuant model on a directed Barabasi-Albert network with discrete opinions and several subjects. Noticed is a focusing of the the resulting opinion distribution during the simulation towards the average value of the initial opinion distribution. A small change of the focusing is seen. A dependency of this change on the number of subjects and opinions is detected and indicates the change as a consequence of discretization the opinions. Hereby the average value of the initial opini…
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.
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…
Convex Regions of Opinion Dynamics, Approaches to the Complexity of Binary Consensus with Reference to Addiction and Obliviousness: Integrated Dimer Model Perspective
本文提出集成二聚体模型，通过计算凸区域的Castellain矩阵、分布函数和二聚体构型概率，并引入依赖性与遗忘因素，研究意见动力学中的二元共识复杂性，为理解社会意见形成提供新方法。
Polemical Case Study of Opinion Dynamics:Patterns of Filter Bubbles in Non-Consensus, Rewire Phenomena
本文通过社会物理学模拟，探讨了在距离、时间、强意见集群等条件下过滤气泡导致意见分歧或趋同但未达成共识的现象，作为相关研究的附录。
Massive Case Study of Opinion Distribution in a Relationship with Mixed Trust and Distrust
本研究基于意见动力学，通过大规模模拟（N=10000与N=3000）验证信任与不信任比例在55%附近的相变现象，为共识建立提供模拟要素参考。
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。
We study an opinion formation model that takes into account that individuals have diverse preferences when forming their opinion regarding a particular issue. We show that the system exhibits a phenomenon called "diversity-induced resonance"[Tessone et al. Phys. Rev. Lett. 97, 194101 (2006)], by which an external influence (for example advertising, or fashion trends) is better followed by populations having the right degree of diversity in their preferences, rather than others where the individuals are identical or have too different preferences. We support our findings by numerical simulation…
A way to simulate the basic interactions between two individuals with different opinions, in the context of strategic game theory, is proposed. Various games are considered, which produce different kinds of opinion formation dynamics. First, by assuming that all individuals (players) are equals, we obtain the bounded confidence model of continuous opinion dynamics proposed by Deffuant et al. In such a model a tolerance threshold is defined, such that individuals with difference in opinion larger than the threshold can not interact. Then, we consider that the individuals have different inclinat…
Kinetic SIS opinion-driven models with asymmetric awareness feedback: macroscopic limit and polarization
本文提出了一种结合意见动态与传染病传播的SIS模型，通过不对称反馈机制研究传染病流行与意见极化之间的相互作用。
Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion. In this case, the agreement is reached because the new arguments are incorporated. In this paper we deal with a simple model of opinion formation with such persuasion dynamics, and we find the exact analytical solutions for both, long and short range interactions. A novel theoretical approach has been used in order to solve the master equations of the model with non-local kernels. S…
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 …
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…
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…
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…
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…
Phase Field Modeling in Social Media Dynamics:Simulation of Opinion Evolution with Feedback, Separation
本研究提出一种基于相场建模的数值模型，利用连续变量表示用户意见，结合确认偏差等心理因素与真实数据，模拟社交网络信息传播与反馈，定量分析意见极化和回音室效应。
Microcanonical Monte Carlo simulation of opinion dynamics under the influence of mass media
本研究将大众媒体作为恒定外场拓展非格点二维Potts模型，通过微正则蒙特卡洛模拟发现对立外部影响下存在观点集群亚稳态，且特定总能量下仅单一统一观点集群稳定存在。
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。
Quantum Simulations of Opinion Dynamics
本研究提出了一种基于量子计算的 opinion dynamics 模型，通过量子叠加和纠缠等机制，系统研究网络连通性对共识形成的影响，并在 IBM 量子设备上验证了其有效性。
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…
In this paper Nowak--Szamrej-Latané model is reconsidered. This computerised model of opinion formation bases on Latané theory of social impact. We modify this model to allow for multi (more than two) opinions. With computer simulations we show that in the modified model the signatures of order/disorder phase transition are still observed. The transition may be observed in the average fraction of actors sharing the $i$-th opinion, its variation and also average number of clusters of actors with the same opinion and the average size of the largest cluster of actors sharing the same opinion. Als…
From Qubits to Opinions: Operator and Error Syndrome Measurement in Quantum-Inspired Social Simulations on Transversal Gates
本文提出一种新颖的量子启发社会模拟框架，利用toric code和transversal gates检测与纠正错误，并借助算子与错误综合征测量分析决策不确定性，从而提升社会模拟中决策与策略形成的保真度。
According to research, reducing consumer energy demand through behavioural interventions is an important factor of efforts to reduce greenhouse gas emissions and climate change.On this basis, feedback interventions that make energy consumption and conservation efforts apparent are seen as a feasible method for increasing energy-saving habits. Simulation techniques provide a convenient and cost-effective tool for examining the parameters that may affect the amount of energy saved as a result of such interventions. However, constructing a reliable model that accurately represents real-world proc…
Modified Axelrod Model Showing Opinion Convergence And Polarization In Realistic Scale-Free Networks
改进的Axelrod模型通过引入无标度网络和有界置信机制，研究意见收敛与极化，并探讨减少极化的有效策略。
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…
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…
We generalize Galam's model of opinion spreading by introducing three competing choices. At each update, the population is randomly divided in groups of three agents, whose members adopt the opinion of the local majority. In the case of a tie, the local group adopts opinion A, B or C with probabilities alpha, beta and (1-alpha-beta) respectively. We derive the associated phase diagrams and dynamics by both analytical means and simulations. Polarization is always reached within very short time scales. We point out situations in which an initially very small minority opinion can invade the whole…
Opinion dynamics models have been developed to study and predict the evolution of public opinion. Intensive research has been carried out on these models, especially exploring the different rules and topologies, which can be considered two degrees of freedom of these models. In this paper we introduce what can be considered a third degree of freedom. Since it is not possible to directly access someone's opinions without measuring them, we always need to choose a way to transform real world opinions (e.g. being anti-Trump) into numbers. However, the properties of this transformation are usually…
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 …
Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks
研究异质空间复杂网络中意见动态的稳定边界，揭示了局部意见域在竞争中持久共存的机制。
We study the Deffuant et al. model for continuous--opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending of a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce an order-disorder transition. In the di…
Opinion Dynamics in Two-Layer Networks with Hypocrisy
本文提出广义隐蔽选民模型（GCVM），允许个体在内部层交换真实观点，通过数值模拟发现外部层结构简单时共识难以达成，且公开表达不佳时内部交流几乎无效。
Modeling Explosive Opinion Depolarization in Interdependent Topics
本文提出 social compass model 研究相互依赖话题的意见去极化动力学，解析证明在话题不相关时从极化到共识的相变具有爆发性，并通过数值模拟与真实选举数据验证了该理论框架。
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