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.     

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.     

The development and interaction of terrorist and fanatic groups

Through the mathematical study of two models we quantify some of the theories of co-development and co-existence of focused groups in the social sciences. This work attempts to develop the mathematical framework behind the social sciences of community formation. By using well developed theories and concepts from ecology and epidemiology we hope to extend the theoretical framework of organizing and self-organizing social groups and communities, including terrorist groups. The main goal of our work is to gain insight into the role of recruitment and retention in the formation and survival of social organizations. Understanding the underlining mechanisms of the spread of ideologies under competition is a fundamental component of this work. Here contacts between core and non-core individuals extend beyond its physical meaning to include indirect interaction and spread of ideas through phone conversations, emails, media sources and other similar mean. This work focuses on the dynamics of formation of interest groups, either ideological, economical or ecological and thus we explore the questions such as, how do interest groups initiate and co-develop by interacting within a common environment and how do they sustain themselves? Our results show that building and maintaining the core group is essential for the existence and survival of an extreme ideology. Our research also indicates that in the absence of competitive ability (i.e., ability to take from the other core group or share prospective members) the social organization or group that is more committed to its group ideology and manages to strike the right balance between investment in recruitment and retention will prevail. Thus under no cross interaction between two social groups a single trade-off (of these efforts) can support only a single organization. The more efforts that an organization implements to recruit and retain its members the more effective it will be in transmitting the ideology to other vulnerable individuals and thus converting them to believers.     

A Bayesian framework for the combination of classifier outputs

We explore a Bayesian framework for constructing combinations of classifier outputs, as a means to improving overall classification results. We propose a sequential Bayesian framework to estimate the posterior probability of being in a certain class given multiple classifiers. This framework, which employs meta-Gaussian modelling but makes no assumptions about the distribution of classifier outputs, allows us to capture nonlinear dependencies between the combined classifiers and individuals. An important property of our method is that it produces a combined classifier that dominates the individuals upon which it is based in terms of Bayes risk, error rate, and receiver operating characteristic (ROC) curve. To illustrate the method, we show empirical results from the combination of credit scores generated from four different scoring models.     

Modeling the influence of social networks and environment on energy balance and obesity

The influence of social networks on the development of obesity has been demonstrated, and several models have been proposed. However, these models are limited since they consider obesity as a ‘contagious’ phenomenon that can be caught if most social contacts are deemed obese. Furthermore, social networks were proposed as a means to mitigate the obesity epidemic, but the interaction of social networks with environmental factors could not yet be explored as it was not accounted for in the current models. We propose a new model of obesity to face these limitations. In our model, individuals influence each other with respect to food intake and physical activity, which may lead to changes depending on the environment, and will impact energy balance and weight. We illustrate the potential of our model via two questions: could we focus on social networks and neglect environmental sources of influence, at least from a modelling viewpoint? Are some social structures less prone to be influenced by their environment? We performed a factorial analysis based on both synthetic and real-world social networks, and found that the environment was a key component behind changes in weight but its contribution was mitigated by structural properties of the population. Furthermore, the contribution of the environment was not dictated by macro-level properties (small-world and scale-free), which suggests that particular patterns of social ties at the micro-level are involved in making populations more resilient to change and less influenced by the environment.     

Interdependent binary choices under social influence: Phase diagram for homogeneous unbiased populations

Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are considered: the nonlocal or group interdependence model is used to study two interrelated groups making the same binary choice and the local or individual interdependence model represents a single group, where agents make two binary choices that depend on each other. For both models, phase diagrams and their implications in socioeconomic contexts are described and compared in the absence of private deterministic utilities (zero opinion fields). © 2012 Wiley Periodicals, Inc. Complexity, 2012     

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.     

Unanimous opinions in social influence networks

In this paper, I show that persons reach unanimous opinions even when they have different initial opinions and different social influences in social influence networks. Friedkin and Johnsen introduced a model of social influence networks, and identified conditions for initially diverse opinions to converge. However, they did not examine conditions of “unanimous” convergence. Hence, I provide sufficient conditions of such unanimous consensus by focusing on three typical but conflicting social influences: the equal influence, the influence of the lowest opinion, and no influence. I show that unanimous opinions occur even when persons have antagonistic social influences such as the equal influence and the influence of the lowest opinion. I also demonstrate that the most cooperative type is the equal influence, but the most central type is the no influence.     

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。     

Multiresolution Network Models

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection-based approaches (e.g., the latent space model in the statistics literature) represent in rich detail the roles of individuals. Many pertinent questions in sociology and economics, however, span multiple scales of analysis. Further, many questions involve comparisons across disconnected graphs that will, inevitably be of different sizes, either due to missing data or the inherent heterogeneity in real-world networks. We propose a class of network models that represent network structure on multiple scales and facilitate comparison across graphs with different numbers of individuals. These models differentially invest modeling effort within subgraphs of high density, often termed communities, while maintaining a parsimonious structure between said subgraphs. We show that our model class is projective, highlighting an ongoing discussion in the social network modeling literature on the dependence of inference paradigms on the size of the observed graph. We illustrate the utility of our method using data on household relations from Karnataka, India. Supplementary material for this article is available online.     

Behavioral modeling in weight loss interventions

Designing systems with human agents is difficult because it often requires models that characterize agents’ responses to changes in the system’s states and inputs. An example of this scenario occurs when designing treatments for obesity. While weight loss interventions through increasing physical activity and modifying diet have found success in reducing individuals’ weight, such programs are difficult to maintain over long periods of time due to lack of patient adherence. A promising approach to increase adherence is through the personalization of treatments to each patient. In this paper, we make a contribution toward treatment personalization by developing a framework for predictive modeling using utility functions that depend upon both time-varying system states and motivational states evolving according to some modeled process corresponding to qualitative social science models of behavior change. Computing the predictive model requires solving a bilevel program, which we reformulate as a mixed-integer linear program (MILP). This reformulation provides the first (to our knowledge) formulation for Bayesian inference that uses empirical histograms as prior distributions. We study the predictive ability of our framework using a data set from a weight loss intervention, and our predictive model is validated by comparison to standard machine learning approaches. We conclude by describing how our predictive model could be used for optimization, unlike standard machine learning approaches that cannot.     

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.     

Chaotic social interaction via endogenous reactivity

We propose a framework to analyse the dynamical process of decision and opinion formation of two economic homogeneous and boundedly rational agents that interact and learn from each other over time. The decisional process described in our model is an adaptive adjustment mechanism in which two agents take into account the difference between their own opinion and the opinion of the other agent. The smaller that difference, the larger the weight given to the comparison of the opinions. We assume that if the distance between the two opinions is larger than a given threshold, then there is no interaction and the agents do not change their opinion anymore. Introducing an auxiliary variable describing the distance between the opinions, we obtain a one-dimensional map for which we investigate, mainly via analytical tools, the stability of the steady states, their bifurcations, as well as the existence of chaotic dynamics and multistability phenomena.     

Pricing range notes within Wishart affine models

We provide analytic pricing formulas for Fixed and Floating Range Accrual Notes within the multifactor Wishart affine framework which extends significantly the standard affine model. Using estimates for three short rate models, two of which are based on the Wishart process whilst the third one belongs to the standard affine framework, we price these structured products using the FFT methodology. Thanks to the Wishart tractability the hedge ratios are also easily computed. As the models are estimated on the same dataset, our results illustrate how the fit discrepancies (meaning differences in the likelihood functions) between models translate in terms of derivatives pricing errors, and we show that the models can produce different price evolutions for the Range Accrual Notes. The differences can be substantial and underline the importance of model risk both from a static and a dynamic perspective. These results are confirmed by an analysis performed at the hedge ratios level.     

Nonparametric Bayesian topic modelling with the hierarchical Pitman–Yor processes

The Dirichlet process and its extension, the Pitman–Yor process, are stochastic processes that take probability distributions as a parameter. These processes can be stacked up to form a hierarchical nonparametric Bayesian model. In this article, we present efficient methods for the use of these processes in this hierarchical context, and apply them to latent variable models for text analytics. In particular, we propose a general framework for designing these Bayesian models, which are called topic models in the computer science community. We then propose a specific nonparametric Bayesian topic model for modelling text from social media. We focus on tweets (posts on Twitter) in this article due to their ease of access. We find that our nonparametric model performs better than existing parametric models in both goodness of fit and real world applications.     

Friendship Networks Through Time: An Actor-Oriented Dynamic Statistical Network Model

We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.     

Non-bossy social classification

We consider the problem of how societies should be partitioned into classes if individuals express their views about who should be put with whom in the same class. A non-bossy social aggregator depends only on those cells of the individual partitions the society members classify themselves in. This fact allows us to concentrate on a corresponding “opinion graph” for each profile of views. By means of natural sovereignty, liberalism, and equal treatment requirements, we characterize the non-bossy aggregators generating partitions in which the social classes are refinements of the weakly connected components of the opinion graph.     

Non-bossy social classification

We consider the problem of how societies should be partitioned into classes if individuals express their views about who should be put with whom in the same class. A non-bossy social aggregator depends only on those cells of the individual partitions the society members classify themselves in. This fact allows us to concentrate on a corresponding “opinion graph” for each profile of views. By means of natural sovereignty, liberalism, and equal treatment requirements, we characterize the non-bossy aggregators generating partitions in which the social classes are refinements of the weakly connected components of the opinion graph.     

Multiplication and comultiplication of beliefs

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to β probability distributions. We compare different types of opinion product and coproduct, and show that they represent very good approximations of the analytical product and coproduct of β probability distributions. We also define division and codivision of opinions, and compare our framework with other logic frameworks for combining uncertain propositions.