Fairness in opinion dynamics

The opinion dynamics studies how a final consensus emerges from a diversified initial configuration. The final result can be an artifact arising in the voting processes and overlook the features of the initial configuration, which leads to the unfair result. We explore the concept of fairness in opinion dynamics and propose a quantitative measurement in a model system, which allows us to reach a final consensus reflecting impartially the major opinion. For a two-choice system, the unfairness alternates with the increase of meeting agents M. With an odd M, the fair results can be expected; with an even M, the unfairness decays monotonically with an increasing M. When the number of choices is larger than two, such an alternating is smeared out. The fairness at an odd M can no longer be reached. The unfairness increases a bit with the increasing number of choices. Similar M-dependence can be observed for different number of choices. We conclude that the number of choices plays a minor role in reaching a fair final consensus. The fairness is mainly controlled by the meeting size.     

Collective beliefs versus individual inflexibility: The unavoidable biases of a public debate

The combined effects of collective beliefs and individual inflexibility in the dynamics of a public debate are investigated using the Galam sequential probabilistic model of opinion dynamics. The study is focused on pair interactions for which the bias produced by collective beliefs is the decisive factor to win the debate. The current value of that bias is a fixed external parameter. It is a constant of the problem not given to change. In contrast, inflexibility is an individual property. It results from external ingredients, which are susceptible to be modified during the debate. More precisely, giving some beliefs we determine the required inflexibility to oppose its associated bias in the debate outcome. The results shed a new and counter intuitive light on paradoxical outcomes of sensitive issues, which are discussed in the public. The cases of global warming issue and debate over evolution are discussed.     

Controlling tax evasion fluctuations

We incorporate the behaviour of tax evasion into the standard two-dimensional Ising model and augment it by providing policy-makers with the opportunity to curb tax evasion via an appropriate enforcement mechanism. We find that tax evasion may vary greatly over time if no measures of control are taken. Furthermore, we show that even minimal audit rates of a tax authority may help to alleviate this problem substantially. Similar results are observed for other network structures.     

Dynamical Galam model

We introduce a model of temporal evolution of political opinions which amounts to a dynamical extension of Galam model in which the proportions of inflexibles are treated as dynamical variables. We find that the critical value of inflexibles in the original Galam model now turns into a fixed point of the system whose stability controls the phase trajectory of the political opinions. The appearance of two phases is found, in which majority-preserving and regime-changing limit cycles are respectively dominant, and the phase transition between them is observed.     

Formation of share market prices under heterogeneous beliefs and common knowledge

Financial economic models often assume that investors know (or agree on) the fundamental value of the shares of the firm, easing the passage from the individual to the collective dimension of the financial system generated by the Share Exchange over time. Our model relaxes that heroic assumption of one unique “true value” and deals with the formation of share market prices through the dynamic formation of individual and social opinions (or beliefs) based upon a fundamental signal of economic performance and position of the firm, the forecast revision by heterogeneous individual investors, and their social mood or sentiment about the ongoing state of the market pricing process. Market clearing price formation is then featured by individual and group dynamics that make its collective dimension irreducible to its individual level. This dynamic holistic approach can be applied to better understand the market exuberance generated by the Share Exchange over time.     

Hierarchical centralities of information transmissions in reaching a consensus

The question, how central indications arise from an undirected environment and lead to collective behaviors, is analyzed based on a simple model of opinion dynamics, called the DeGroot model. We first reformulate the necessary and sufficient condition for reaching a consensus, then the condition is used to set up the pattern of information transmissions. By classifying the individuals into a sequential series of classes and by giving the dynamic contents of centrality, we demonstrate that the hierarchical centralities with descend strength are associated with the sequential series of classes in information transmissions. The results provide wide applications in social engineering, an example about the merger of different groups is discussed.     

Effects of attachment preferences on coevolution of opinions and networks

In the coevolution of network structures and opinion formation, we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures. It has been found that a heterogeneous network structure is easier to be reached with more high-degree-preferential (HDP) nodes. There exists high correlation between the convergence time and the network heterogeneity. The heterogeneous degree distribution caused by preferential attachment accelerates the convergence to a consensus state and the shortened convergence time inhibits the occurrence of the following disquieting situation that occurs in a continuously evolving network: with preferential attachment and long-time evolvement, most of the nodes would become separated and only a few leaders would have immediate neighbors. Analytical calculations based on mean field theory reveal that both the transition point p_tr and the consensus time τ depend upon the standard deviation of the degree distribution σ_d. p_tr increases while τ decreases with the rise of σ_d. Functions of p_tr=〈k〉/(〈k〉+1) and are found. Theoretical analyses are in accordance with simulation data.     

Effects of selective attention on continuous opinions and discrete decisions

Selective attention describes that individuals have a preference on information according to their involving motivation. Based on achievements of social psychology, we propose an opinion interacting model to improve the modeling of individuals’ interacting behaviors. There are two parameters governing the probability of agents interacting with opponents, i.e. individual relevance and time-openness. It is found that, large individual relevance and large time-openness advance the appearance of large clusters, but large individual relevance and small time-openness favor the lessening of extremism. We also put this new model into application to work out some factor leading to a successful product. Numerical simulations show that selective attention, especially individual relevance, cannot be ignored by launcher firms and information spreaders so as to attain the most successful promotion.     

A Hybrid Opinion Formation and Polarization Model

The last decade has witnessed a great number of opinion formation models that depict the evolution of opinions within a social group and make predictions about the evolution process. In the traditional formulation of opinion evolution such as the DeGroot model, an agent’s opinion is represented as a real number and updated by taking a weighted average of its neighbour’s opinions. In this paper, we adopt a hybrid representation of opinions that integrate both the discrete and continuous nature of an opinion. Basically, an agent has a ‘Yes’, ‘Neutral’ or ‘No’ opinion on some issues of interest and associates with its Yes opinion a support degree which captures how strongly it supports the opinion. With such a rich representation, not only can we study the evolution of opinion but also that of support degree. After all, an agent’s opinion can stay the same but become more or less supportive of it. Changes in the support degree are progressive in nature and only a sufficient accumulation of such a progressive change will result in a change of opinion say from Yes to No. Hence, in our formulation, after an agent interacts with another, its support degree is either strengthened or weakened by a predefined amount and a change of opinion may occur as a consequence of such progressive changes. We carry out simulations to evaluate the impacts of key model parameters including (1) the number of agents, (2) the distribution of initial support degrees and (3) the amount of change of support degree changes in a single interaction. Last but not least, we present several extensions to the hybrid and progressive model which lead to opinion polarization.     

社会群体中观点的信任、演化与共识

针对连续观点动力学模型中缺乏对个体信任及其观点的不同权重的考虑,本文通过扩展HegselmannKrause模型,引入个体间的信任度和观点间的相似度,将有限信任假设扩展为有限影响假设,建立带权重的观点更新模型,以研究社会群体中少数的偏执个体和权威个体对观点形成、演化以及共识构建过程的影响.仿真结果表明,这两类个体的初始观点尽量接近观点分布区间中点0.5或者增加偏执个体的影响阈值和权威个体的可信任程度可以使群体形成更少和更大的观点簇.随着偏执个体的影响阈值增加,最大簇的观点位置集中于0.5附近;而增加权威个体的可信任程度,最大簇的观点不断接近权威个体的最终观点.模型结果能够在一定程度上反映和解释现实社会中偏执个体和权威个体现象.     

Chaos in social learning with multiple true states

Most existing social learning models assume that there is only one underlying true state. In this work, we consider a social learning model with multiple true states, in which agents in different groups receive different signal sequences generated by their corresponding underlying true states. Each agent updates his belief by combining his rational self-adjustment based on the external signals he received and the influence of his neighbors according to their communication. We observe chaotic oscillation in the belief evolution, which implies that neither true state could be learnt correctly by calculating the largest Lyapunov exponents and Hurst exponents.     

A model of the effects of authority on consensus formation in adaptive networks: Impact on network topology and robustness

Opinions of individuals in real social networks are arguably strongly influenced by external determinants, such as the opinions of those perceived to have the highest levels of authority. In order to model this, we have extended an existing model of consensus formation in an adaptive network by the introduction of a parameter representing each agent’s level of ‘authority’, based on their opinion relative to the overall opinion distribution. We found that introducing this model, along with a randomly varying opinion convergence factor, significantly impacts the final state of converged opinions and the number of interactions required to reach that state. We also determined the relationship between initial and final network topologies for this model, and whether the final topology is robust to node removals. Our results indicate firstly that the process of consensus formation with a model of authority consistently transforms the network from an arbitrary initial topology to one with distinct measurements in mean shortest path, clustering coefficient, and degree distribution. Secondly, we found that subsequent to the consensus formation process, the mean shortest path and clustering coefficient are less affected by both random and targeted node disconnection. Speculation on the relevance of these results to real world applications is provided.     

Public debates driven by incomplete scientific data: The cases of evolution theory, global warming and H1N1 pandemic influenza

Public debates driven by incomplete scientific data where nobody can claim absolute certainty, due to the current state of scientific knowledge, are studied. The cases of evolution theory, global warming and H1N1 pandemic influenza are investigated. The first two are of controversial impact while the third is more neutral and resolved. To adopt a cautious balanced attitude based on clear but inconclusive data appears to be a lose-out strategy. In contrast overstating arguments with incorrect claims which cannot be scientifically refuted appears to be necessary but not sufficient to eventually win a public debate. The underlying key mechanisms of these puzzling and unfortunate conclusions are identified using the Galam sequential probabilistic model of opinion dynamics (Galam, 2002 [4], Galam, 2005 [18], Galam and Jacobs, 2007 [19]). It reveals that the existence of inflexible agents and their respective proportions are the instrumental parameters to determine the faith of incomplete scientific data in public debates. Acting on one’s own inflexible proportion modifies the topology of the flow diagram, which in turn can make irrelevant initial supports. On the contrary focusing on open-minded agents may be useless given some topologies. When the evidence is not as strong as claimed, the inflexibles rather than the data are found to drive the opinion of the population. The results shed a new but disturbing light on designing adequate strategies to win a public debate.     

Continuous opinion model in small-world directed networks

In the compromise model of continuous opinions proposed by Deffuant et al., the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance ?. In directed networks, if agent i is a neighbor of agent j,j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions 〈F〉 and their distribution as a function of ? and of the network structural disorder. In directed networks 〈F〉 exhibits a rich structure, being larger than in undirected networks for higher values of ?, and smaller for lower values of ?.     

Restoration of a Poisson distributed image using a principle of extreme physical information

Suppose that an object which reflects or emits light is captured by a sensor. The image data are distorted in various ways. The aim is to restore the object. For this purpose, a new restoration method is devised. It uses the Fisher-information based principle of extreme physical information (EPI). This solves a variational problem I − J = extremum, expressing a flow of information J → I from source to output in the restoration problem. Here, the source of information is the Poissonian image data, and J is modeled as its Hartley information level. Also, I is the Fisher information in the output restored object. The approach dates from the 1980s. It has been already shown that many fundamental physical laws may be derived using EPI. In this paper, the EPI approach is applied to the restoration problem, wherein it regards the unknown restoration as another fundamental law. It models the source information J as obeying Poisson statistics, and assumes additional image distortions that are due to additive Gaussian noise and quantization of the image data. It is found that the quantization level determines the degree of smoothness (or sharpness) of the restored signal. An optimal level of image quantization can be accomplished by adjusting its cross entropy. Finally, the restoration method by EPI is validated by numerical simulations of the image forming and restoring system.     

Statistical physics of media processes: Mediaphysics

The processes of mass communications in complicated social or sociobiological systems such as marketing, economics, politics, animal populations, etc. as a subject for the special scientific subbranch—“mediaphysics”—are considered in its relation with sociophysics. A new statistical physics approach to analyze these phenomena is proposed. A keystone of the approach is an analysis of population distribution between two or many alternatives: brands, political affiliations, or opinions. Relative distances between a state of a “person's mind” and the alternatives are measures of propensity to buy (to affiliate, or to have a certain opinion). The distribution of population by those relative distances is time dependent and affected by external (economic, social, marketing, natural) and internal (influential propagation of opinions, “word of mouth”, etc.) factors, considered as fields. Specifically, the interaction and opinion-influence field can be generalized to incorporate important elements of Ising-spin-based sociophysical models and kinetic-equation ones. The distributions were described by a Schrödinger-type equation in terms of Green's functions. The developed approach has been applied to a real mass-media efficiency problem for a large company and generally demonstrated very good results despite low initial correlations of factors and the target variable.     

漫谈社会物理学

进入21世纪以来,社会系统的复杂性已经逐步成为科学研究的热点领域,社会物理学利用物理学的思想和方法研究社会问题,已经取得了不少成果.文章首先简要回顾了社会物理学发展的历史,然后简要介绍了当代社会物理学的研究问题和成果,主要包括行人动力学、社会网络分析和舆论动力学三个方面.涉及社会力作用下行人的运动以及所表现出的群体行为、社会网络结构分析的基本概念,特别是社团结构的定义及其探测方法、基于自旋相互作用的舆论形成模型和相变行为等.     

漫谈社会物理学

进入21世纪以来,社会系统的复杂性已经逐步成为科学研究的热点领域,社会物理学利用物理学的思想和方法研究社会问题,已经取得了不少成果.文章首先简要回顾了社会物理学发展的历史,然后简要介绍了当代社会物理学的研究问题和成果,主要包括行人动力学、社会网络分析和舆论动力学三个方面.涉及社会力作用下行人的运动以及所表现出的群体行为、社会网络结构分析的基本概念,特别是社团结构的定义及其探测方法、基于自旋相互作用的舆论形成模型和相变行为等.     

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.