Meet,discuss, and segregate!

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions toward an average opinion, whereas low thresholds result in several opinion clusters. The model is further generalized to network interactions, threshold heterogeneity, adaptive thresholds, and binary strings of opinions. © 2002 Wiley Periodicals, Inc.     

No place like home: Opinion formation with homophily and implications for policy decisions

We set up an opinion diffusion model with a local opinion leader, and using simulations we show the possibility of driving a significant wedge between the opinions of two groups that exhibit homophily although individuals are highly conformist. There exists an opinion gap between the group to which the opinion leader belongs and the other group. This opinion gap increases according to the relative size of the residence community. We show empirical traits related to our simulation: Employing Swiss national referenda data from 2008 to 2012, we show that members of parliament match referenda outcomes in their residence communities closer than they do in neighboring communities and that this wedge interacts significantly with the relative size of the residence community.     

Minorities in a model for opinion formation

We study a model for social influence in which the agents' opinion is a continuous variable [G. Weisbuch et al., Complexity 2002, 7(2), 55]. The convergent opinion adjustment process takes place as a result of random binary encounters whenever the difference between agents' opinions is below a given threshold. The inhomogeneity in the dynamics gives rise to a complex steady state structure, which is also highly dependent on the threshold and on the convergence parameter of the model. © 2004 Wiley Periodicals, Inc. Complexity 9: 24–30, 2004     

Opinion polarization by learning from social feedback

We explore a new mechanism to explain polarization phenomena in opinion dynamics in which agents evaluate alternative views on the basis of the social feedback obtained on expressing them. High support of the favored opinion in the social environment is treated as a positive feedback which reinforces the value associated to this opinion. In connected networks of sufficiently high modularity, different groups of agents can form strong convictions of competing opinions. Linking the social feedback process to standard equilibrium concepts we analytically characterize sufficient conditions for the stability of bi-polarization. While previous models have emphasized the polarization effects of deliberative argument-based communication, our model highlights an affective experience-based route to polarization, without assumptions about negative influence or bounded confidence.     

Innovation governs everything eventually: Extensions of the DeGroot model

We study the DeGroot model for continuous opinion dynamics under the influence of innovations. In the original model, individuals’ opinions, after given their initial values, evolve merely according to the given learning topology. The main contribution of this paper is that external innovation effects are introduced: each individual is given the opportunity to change her opinion to a randomly selected opinion according to a given distribution on the opinion space and then the external opinion is either adapted by the individual, or combined into her learning process. It turns out that all the classical results of the DeGroot model are violated in this new model. We prove that convergence can still be guaranteed in the expectation sense, regardless of the learning topology. We also study the steady distributions of opinions among the society and the time spent to reach a steady state by means of Monte-Carlo simulations.     

A hybrid model for opinion formation

This paper presents a hybrid model for opinion formation in a large group of agents exposed to the persuasive action of a small number of strong opinion leaders. The model is defined by coupling a finite difference equation for the dynamics of leaders opinion with a continuous integro-differential equation for the dynamics of the others. Such a definition stems from the idea that the leaders are few and tend to retain original opinions, so that their dynamics occur on a longer time scale with respect to the one of the other agents. A general well-posedness result is established for the initial value problem linked to the model. The asymptotic behavior in time of the related solution is characterized for some general parameter settings, which mimic distinct social scenarios, where different emerging behaviors can be observed. Analytical results are illustrated and extended through numerical simulations.     

Dissonance Minimization as a Microfoundation of Social Influence in Models of Opinion Formation

Models of opinion formation are used to investigate many collective phenomena. While social influence often constitutes a basic mechanism, its implementation differs between the models. In this article, we provide a general framework of social influence based on dissonance minimization. We only premise that individuals strive to minimize dissonance resulting from different opinions compared to individuals in a given social network. Within a game theoretic context, we show that our concept of dissonance minimization resembles a coordination process when interactions are homogeneous. We further show that different models of opinion formation can be represented as best response dynamics within our framework. Thus, we offer a unifying perspective on these heterogeneous models and link them to rational choice theory.     

Deffuant model with general opinion distributions: First impression and critical confidence bound

In the Deffuant model for social influence, pairs of adjacent agents interact at a constant rate and mix up their opinions (represented by continuous variables) only if the distance between opinions is short according to a threshold. We derive a critical threshold for the Deffuant model on , above which the opinions converge toward the average value of the initial opinion distribution with probability one, provided the initial distribution has a finite second order moment. We demonstrate our theoretical results by performing extensive numerical simulations on some continuous probability distributions including uniform, Beta, power‐law and normal distributions. Noticed is a clear differentiation of convergence rate that unimodal opinions (regardless of being biased or not) achieve consensus much faster than even or polarized opinions. Hereby, the emergence of a single mainstream view is a prominent feature giving rise to fast consensus in public opinion formation and social contagious behavior. Finally, we discuss the Deffuant model on an infinite Cayley tree, through which general network architectures might be factored in. © 2013 Wiley Periodicals, Inc. Complexity 19: 38–49, 2013     

Some remarks on the concept of proportionality

Proportionality plays a role in many principles of fairness or justice. In particular, it is often invoked in electoral systems aiming at a similarity of opinion distributions in the parliament and in the electorate at large. The proportional systems of representation (PR systems, for short) strive for maximal similarity between these two distributions. Unfortunately, the concept of proportionality is imprecise in two senses: it is vague and ambiguous. In other words, once a clear criterion of what we mean by proportionality is given, different PR systems may differ in the degree of proportionality achieved in any given election. This is what will be referred to as the vagueness of proportionality (of election outcomes). Proportionality is, however, also ambiguous in that it refers to different things depending on how the voters are expected to signal their opinions and on what is it that one wishes to distribute proportionally.     

Opinion transmission in organizations: an agent-based modeling approach

This paper builds a theoretical framework to detect the conditions under which social influence enables persistence of a shared opinion among members of an organization over time, despite membership turnover. It develops agent-based simulations of opinion evolution in an advice network, whereby opinion is defined in the broad sense of shared understandings on a matter that is relevant for an organization’s activities, and on which members have some degree of discretion. We combine a micro-level model of social influence that builds on the “relative agreement” approach of Deffuant et al. (J. Artif. Soc. Simul. 5:4, 2002), and a macro-level structure of interactions that includes a flow of joiners and leavers and allows for criteria of advice tie formation derived from, and grounded in, the empirical literature on intra-organizational networks. We provide computational evidence that persistence of opinions over time is possible in an organization with joiners and leavers, a result that depends on circumstances defined by mode of network tie formation (in particular, criteria for selection of advisors), individual attributes of agents (openness of newcomers to influence, as part of their socialization process), and time-related factors (turnover rate, which regulates the flow of entry and exit in the organization, and establishes a form of endogenous hierarchy based on length of stay). We explore the combined effects of these factors and discuss their implications.     

Inferring probability densities from expert opinion

When experts are asked to assess a situation, they often express their opinions providing estimates of the probability of observing the occurrence of a random variable in given intervals, sometimes up to a range of values, rather than simply providing point estimates. The problem we face is how to translate that expert opinion into probability distributions. We examine a novel way of solving that problem by making use of the maximum entropy method in the data to deal with expert opinions expressed with or without uncertainty bands. Our method allows us to unveil underlying probability distributions driving expert opinions expressed with and without uncertainty.     

A model of influence based on aggregation functions

The paper concerns a dynamic model of influence in which agents make a yes–no decision. Each agent has an initial opinion which he may change during different phases of interaction, due to mutual influence among agents. We investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents. Our framework covers numerous existing models of opinion formation, since we allow for arbitrary aggregation functions. We provide a general analysis of convergence in the aggregation model and find all terminal classes and states. We show that possible terminal classes to which the process of influence may converge are terminal states (the consensus states and nontrivial states), cyclic terminal classes, and unions of Boolean lattices (called regular terminal classes). An agent is influential for another agent if the opinion of the first one matters for the latter. A generalization of influential agent to an irreducible coalition whose opinion matters for an agent is called influential coalition. The graph (hypergraph) of influence is a graphical representation of influential agents (coalitions). Based on properties of the hypergraphs of influence we obtain conditions for the existence of the different kinds of terminal classes. An important family of aggregation functions–the family of symmetric decomposable models–is discussed. Finally, based on the results of the paper, we analyze the manager network of Krackhardt.     

基于直觉模糊距离的群决策专家意见聚合分析

提出了一种基于直觉模糊距离来聚合专家个人意见为一个优化的群体意见一致度的新方法.首先,根据直觉模糊集的几何意义,定义了两个直觉模糊集之间的距离;然后,利用直觉模糊距离来聚合专家两两之间对备选方案意见的一致度,综合考虑每位专家的相对重要权重,得到专家群体对备选方案意见的综合一致度;最后通过一个具体实例来说明这种方法的具体应用及计算过程.     

Optimal control of the freezing time in the Hegselmann–Krause dynamics

We study the optimal control problem of minimizing the freezing time in the discrete Hegselmann–Krause (HK) model of opinion dynamics. The underlying model is extended with a set of strategic agents that can freely place their opinion at every time step. Indeed, if suitably coordinated, the strategic agents can significantly lower the freezing time of an instance of the HK model. We give several lower and upper worst-case bounds for the freezing time of a HK system with a given number of strategic agents, while still leaving some gaps for future research.     

Linguistic group decision-making: opinion aggregation and measures of consensus

Group decision-making is a crucial activity, necessary in many aspects of our civilization. In many cases, due to inherent complexity, experts cannot express their opinion or preferences using exact numbers, thus resorting to a qualitative preference such as linguistic labels. Another complicating factor is the fact that very seldom all individuals in a group share the same opinion about the alternatives. This creates the need to aggregate all the differing individual opinions into a group opinion. Moreover, it is desirable to be able to assess the level of agreement among the experts; termed consensus. This paper presents a methodology for aggregating experts’ judgements, presented as linguistic labels, into a group opinion with a measure of the group consensus. The aggregation model allows weighted experts to express a degree of optimism or upward bias in their opinions. Then the paper presents two models of calculating the consensus based on the individual expert opinions and the group aggregated opinion.     

An evidential opinion dynamics model based on heterogeneous social influential power

This paper introduces an evidential opinion dynamics model combing Dempster–Shafer evidence theory to explore the opinion evolution. Our model is an improvement of the Continuous Opinions and Discrete Actions (CODA) model. The process of people updating their opinions is regarded as a decision making process. The unavoidable uncertainty of the opinion evolution is handled by Dempster–Shafer evidence theory. Thereby, a new opinion group, i.e.the neutrals, is introduced into the system. Simulations show the neutral group plays a significant part in the opinion evolution. An opinion ice-breaking process at the early stage of the opinion evolution is observed. It is found that the consensus is not always reached then clusters emerge instead, which depends on the proportions of supporters, neutrals and opponents. The individual’s influential power is taken into account. With the positive feedback mechanism of people’s influential power, the obtained results are in accordance with people’s daily cognition such as the Authority Effect and the Matthew Effect. The final influential power distribution of all individuals in our model presents power-law characteristic.     

不同信任环境下在线知识社区知识系统演化研究

信任作为在线知识社区中的社会影响因素,对社区中的成员进行沟通学习、知识共享有着重要的作用。不同的在线知识社区有着不同的信任环境,而信任环境的不同会影响社区中用户的学习模式和观点传播。基于此,本文提出了基于信任与Deffaunt的组合观点影响模型。信任模型主要将社区中的信任分为认知信任和情感信任,通过调节参数结构,对应不同信任环境中信任的动态演化过程。Deffaunt模型作为基本观点影响模型,模拟了不同信任环境下的在线知识社区的知识观点的演化过程。实验结果发现,信任环境的高低决定了社区中的观点是否收敛,并且社区中的群体理性人占比和信任程度都能影响观点的收敛速度。     

On optimal partitions,individual values and cooperative games: Does a wiser agent always produce a higher value?

We consider an optimal partition of resources (e.g. consumers) between several agents, given utility functions (“wisdoms”) for the agents and their capacities. This problem is a variant of optimal transport (Monge–Kantorovich) between two measure spaces where one of the measures is discrete (capacities) and the costs of transport are the wisdoms of the agents. We concentrate on the individual value for each agent under optimal partition and show that, counter-intuitively, this value may decrease if the agent’s wisdom is increased. Sufficient and necessary conditions for the monotonicity with respect to the wisdom functions of the individual values will be given, independently of the other agents. The sharpness of these conditions is also discussed. Motivated by the above we define a cooperative game based on optimal partition and investigate conditions for stability of the grand coalition.     

Per una teoria delle classi comunque grandi

We propose an axiomatic theory about this work based upon an original way intending the belonging idea. We think it would be necessary to distinguish among several uses of the word belonging, till now expressed by Peano's symbol. This theory is called “The theory of classes however the large ones» because we think that it comes up to the necessity don't to restrict the size of classes which are expressible by a foundational theory. It is a first order theory, showed by eight axioms; it alphabet includes a lot of infinitely simbols of belonging, one for each level, distinguished one from each other. We think that introducing a lot of symbols we can avoid the classical antinomies and we can extend the Von Neumann's process till we need. The last one restricted to distinguish between the sets and the proper classes. For us this becomes the distinction between the first and the second level. In fact this theory develops the main idea of N.B.C.'s according to which a proper class never belongs to some other class. According to our opinion a class can belong to a larger one because it is a different belonging from the belonging that exists between a set and a proper class.     

投资者看法差异与风险资产定价

股票市场中投资者的看法差异是否影响定价?将投资者之间由于信息不对称引起的看法差异和对称信息下由于信念异质引起的看法差异,纳入统一的一个理性预期模型,推导出基于信息性风险和异质信念下的风险资产定价模型,对几种不同来源性质的看法差异进行剥离并通过对均衡价格的比较静态分析证明了:由信息不对称造成的看法差异与投资者要求的预期收益率正相关,而由信念异质引起的看法差异与预期收益率负相关.这表明:投资者对逆向选择风险要求额外的风险贴水,而相反会忽视赢者诅咒风险,投资者的看法差异越大越会造成股票价格的高估.