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Noah E Friedkin - One of the best experts on this subject based on the ideXlab platform.
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Social Power Dynamics Over Switching and Stochastic Influence Networks
IEEE Transactions on Automatic Control, 2019Co-Authors: Ge Chen, Noah E Friedkin, Xiaoming Duan, Francesco BulloAbstract:The DeGroot–Friedkin (DF) model is a recently proposed dynamical description of the evolution of individuals’ self-appraisal and social power in a social Influence Network. Most studies of this system and its variations have so far focused on models with a time-invariant Influence Network. This paper proposes novel models and analysis results for DF models over switching Influence Networks, and with or without environment noise. First, for a DF model over switching Influence Networks, we show that the trajectory of the social power converges to a ball centered at the equilibrium reached by the original DF model. For the DF model with memory on random interactions, we show that the social power converges to the equilibrium of the original DF model almost surely. Additionally, this paper studies a DF model that contains random interactions and environment noise, and has memory on the self-appraisal. We show that such a system converges to an equilibrium or a set almost surely. Finally, as a by-product, we provide novel results on the convergence rates of the original DF model and convergence results for a continuous-time DF model.
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Opinion evolution in time-varying social Influence Networks with prejudiced agents
IFAC-PapersOnLine, 2017Co-Authors: Anton V. Proskurnikov, Ming Cao, Roberto Tempo, Noah E FriedkinAbstract:Abstract Investigation of social Influence dynamics requires mathematical models that are “simple” enough to admit rigorous analysis, and yet sufficiently “rich” to capture salient features of social groups. Thus, the mechanism of iterative opinion pooling from (DeGroot, 1974), which can explain the generation of consensus, was elaborated in (Friedkin and Johnsen, 1999) to take into account individuals’ ongoing attachments to their initial opinions, or prejudices. The “anchorage” of individuals to their prejudices may disable reaching consensus and cause disagreement in a social Influence Network. Further elaboration of this model may be achieved by relaxing its restrictive assumption of a time-invariant Influence Network. During opinion dynamics on an issue, arcs of interpersonal Influence may be added or subtracted from the Network, and the Influence weights assigned by an individual to his/her neighbors may alter. In this paper, we establish new important properties of the (Friedkin and Johnsen, 1999) opinion formation model, and also examine its extension to time-varying social Influence Networks.
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Opinion Dynamics and Social Power Evolution over Reducible Influence Networks
SIAM Journal on Control and Optimization, 2017Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:Our recent work [Jia et al., SIAM Rev., 57 (2015), pp. 367--397] proposes the DeGroot--Friedkin dynamical model for the analysis of social Influence Networks. This dynamical model describes the evolution of self-appraisals in a group of individuals forming opinions in a sequence of issues. Under a strong connectivity assumption, the model predicts the existence and semiglobal attractivity of equilibrium configurations for self-appraisals and social power in the group. In this paper, we extend the analysis of the DeGroot--Friedkin model to two general scenarios where the interpersonal Influence Network is not necessarily strongly connected and where the individuals form opinions with reducible relative interactions. In the first scenario, the relative interaction digraph is reducible with globally reachable nodes; in the second scenario, the condensation of the relative interaction digraph has multiple aperiodic sinks. For both scenarios, we provide the explicit mathematical formulations of the DeGroot--Fr...
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a theory of the evolution of social power natural trajectories of interpersonal Influence systems along issue sequences
Sociological Science, 2016Co-Authors: Noah E Friedkin, Francesco BulloAbstract:This article reports new advancements in the theory of Influence system evolution in small deliberative groups, and a novel set of empirical findings on such evolution. The theory elaborates the specification of the single-issue opinion dynamics of such groups, which has been the focus of theory development in the field of opinion dynamics, to include group dynamics that occur along a sequence of issues. The theory predicts an evolution of Influence centralities along issue sequences based on elementary reflected appraisal mechanisms that modify Influence Network structure and flows of Influence in the group. The new empirical findings, which are also reported in this article, present a remarkable suite of issue-sequence effects on Influence Network structure consistent with theoretical predictions.
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opinion dynamics and the evolution of social power in Influence Networks
Siam Review, 2015Co-Authors: Anahita Mirtabatabaei, Noah E Friedkin, Francesco BulloAbstract:This paper studies the evolution of self-appraisal, social power, and interpersonal Influences for a group of individuals who discuss and form opinions about a sequence of issues. Our empirical model combines the averaging rule of DeGroot to describe opinion formation processes and the reflected appraisal mechanism of Friedkin to describe the dynamics of individuals' self-appraisal and social power. Given a set of relative interpersonal weights, the DeGroot--Friedkin model predicts the evolution of the Influence Network governing the opinion formation process. We provide a rigorous mathematical formulation of the Influence Network dynamics, characterize its equilibria, and establish its convergence properties for all possible structures of the relative interpersonal weights and corresponding eigenvector centrality scores. The model predicts that the social power ranking among individuals is asymptotically equal to their centrality ranking, that social power tends to accumulate at the top of the hierarchy,...
Francesco Bullo - One of the best experts on this subject based on the ideXlab platform.
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Social Power Dynamics Over Switching and Stochastic Influence Networks
IEEE Transactions on Automatic Control, 2019Co-Authors: Ge Chen, Noah E Friedkin, Xiaoming Duan, Francesco BulloAbstract:The DeGroot–Friedkin (DF) model is a recently proposed dynamical description of the evolution of individuals’ self-appraisal and social power in a social Influence Network. Most studies of this system and its variations have so far focused on models with a time-invariant Influence Network. This paper proposes novel models and analysis results for DF models over switching Influence Networks, and with or without environment noise. First, for a DF model over switching Influence Networks, we show that the trajectory of the social power converges to a ball centered at the equilibrium reached by the original DF model. For the DF model with memory on random interactions, we show that the social power converges to the equilibrium of the original DF model almost surely. Additionally, this paper studies a DF model that contains random interactions and environment noise, and has memory on the self-appraisal. We show that such a system converges to an equilibrium or a set almost surely. Finally, as a by-product, we provide novel results on the convergence rates of the original DF model and convergence results for a continuous-time DF model.
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Opinion Dynamics and Social Power Evolution over Reducible Influence Networks
SIAM Journal on Control and Optimization, 2017Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:Our recent work [Jia et al., SIAM Rev., 57 (2015), pp. 367--397] proposes the DeGroot--Friedkin dynamical model for the analysis of social Influence Networks. This dynamical model describes the evolution of self-appraisals in a group of individuals forming opinions in a sequence of issues. Under a strong connectivity assumption, the model predicts the existence and semiglobal attractivity of equilibrium configurations for self-appraisals and social power in the group. In this paper, we extend the analysis of the DeGroot--Friedkin model to two general scenarios where the interpersonal Influence Network is not necessarily strongly connected and where the individuals form opinions with reducible relative interactions. In the first scenario, the relative interaction digraph is reducible with globally reachable nodes; in the second scenario, the condensation of the relative interaction digraph has multiple aperiodic sinks. For both scenarios, we provide the explicit mathematical formulations of the DeGroot--Fr...
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a theory of the evolution of social power natural trajectories of interpersonal Influence systems along issue sequences
Sociological Science, 2016Co-Authors: Noah E Friedkin, Francesco BulloAbstract:This article reports new advancements in the theory of Influence system evolution in small deliberative groups, and a novel set of empirical findings on such evolution. The theory elaborates the specification of the single-issue opinion dynamics of such groups, which has been the focus of theory development in the field of opinion dynamics, to include group dynamics that occur along a sequence of issues. The theory predicts an evolution of Influence centralities along issue sequences based on elementary reflected appraisal mechanisms that modify Influence Network structure and flows of Influence in the group. The new empirical findings, which are also reported in this article, present a remarkable suite of issue-sequence effects on Influence Network structure consistent with theoretical predictions.
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opinion dynamics and the evolution of social power in Influence Networks
Siam Review, 2015Co-Authors: Anahita Mirtabatabaei, Noah E Friedkin, Francesco BulloAbstract:This paper studies the evolution of self-appraisal, social power, and interpersonal Influences for a group of individuals who discuss and form opinions about a sequence of issues. Our empirical model combines the averaging rule of DeGroot to describe opinion formation processes and the reflected appraisal mechanism of Friedkin to describe the dynamics of individuals' self-appraisal and social power. Given a set of relative interpersonal weights, the DeGroot--Friedkin model predicts the evolution of the Influence Network governing the opinion formation process. We provide a rigorous mathematical formulation of the Influence Network dynamics, characterize its equilibria, and establish its convergence properties for all possible structures of the relative interpersonal weights and corresponding eigenvector centrality scores. The model predicts that the social power ranking among individuals is asymptotically equal to their centrality ranking, that social power tends to accumulate at the top of the hierarchy,...
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ACC - On the dynamics of Influence Networks via reflected appraisal
2013 American Control Conference, 2013Co-Authors: Peng Jia, Noah E Friedkin, Anahita Mirtabatabaei, Francesco BulloAbstract:In any modern society, individuals interact to form opinions on various topics, including economic, political, and social aspects. Opinions evolve as the result of the continuous exchange of information among individuals where interpersonal Influences play the key role. The study of Influence Network evolution has wide applications in the field of social organization and social psychology. A compelling model is Friedkin's reflected appraisal model where each individual's self-appraisal is set equal to the relative control and power that the agent exerted over prior issue outcomes. Motivated by this empirical framework, we (i) present a rigorous mathematical formulation of the reflected appraisal Influence Network dynamics, (ii) study the equilibria and the convergence properties of the dynamical Influence systems, and (iii) construct the social conditions leading to the emergence of single opinion leaders, clusters of leaders, or diffuse and democratic power structures. In particular, an appropriately-defined eigenvector centrality of the Influence Network is proved to determine each individual's social power and self-appraisal evolution, and then determine the opinion formulation of the whole Network.
Walter Fontana - One of the best experts on this subject based on the ideXlab platform.
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the kappa platform for rule based modeling
Intelligent Systems in Molecular Biology, 2018Co-Authors: Pierre Boutillier, Jean Krivine, Mutaamba Maasha, Xing Li, Hector F Medinaabarca, Jerome Feret, Ioana Cristescu, Angus G Forbes, Walter FontanaAbstract:Motivation: We present an overview of the Kappa platform, an integrated suite of analysis and visualization techniques for building and interactively exploring rule-based models. The main components of the platform are the Kappa Simulator, the Kappa Static Analyzer, and the Kappa Story Extractor. In addition to these components, we describe the Kappa User Interface, which includes a range of interactive visualization tools for rule-based models needed to make sense of the complexity of biological systems. We argue that, in this approach, modeling is akin to programming and can likewise benefit from an integrated development environment. Our platform is a step in this direction. Results: We discuss details about the computation and rendering of static, dynamic, and causal views of a model, which include the contact map, snaphots at different resolutions, the dynamic Influence Network, and causal compression. We provide use cases illustrating how these concepts generate insight. Specifically, we show how the contact map and snapshots provide information about systems capable of polymerization, such as Wnt signaling. A well-understood model of the KaiABC oscillator, translated into Kappa from the literature, is deployed to demonstrate the dynamic Influence Network and its use in understanding systems dynamics. Finally, we discuss how pathways might be discovered or recovered from a rule-based model by means of causal compression, as exemplified for early events in EGF signaling. Availability: The Kappa platform is available via the project website at kappalanguage.org. All components of the platform are open source and freely available through the authors' code repositories.
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Dynamic Influence Networks for Rule-Based Models
IEEE Transactions on Visualization and Computer Graphics, 2018Co-Authors: Angus Forbes, Andrew Burks, Kristine Lee, Pierre Boutillier, Jean Krivine, Walter FontanaAbstract:Fig. 1. A screenshot of the DIN-Viz application for analyzing the dynamics of a rule-based model of a protein-protein interaction Network (i.e., a Dynamic Influence Network). Our approach emphasizes the Influence rules have on each other and enables users to analyze the dynamics of these Influences as they change over time. The left panel shows a Network of interconnected rules at a specific time step. The right panel provides a global overview of the system as well as detailed information about selected rules.
Eugene C Johnsen - One of the best experts on this subject based on the ideXlab platform.
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social Influence Network theory a sociological examination of small group dynamics
2011Co-Authors: Noah E Friedkin, Eugene C JohnsenAbstract:Part I. Introduction: 1. Group dynamics: structural social psychology 2. Formalization: attitude change in Influence Networks 3. Operationalization: constructs and measures 4. Assessing the model Part II. Influence Network Perspective on Small Groups: 5. Consensus formation and efficiency 6. The smallest group 7. Social comparison theory 8. Minority and majority factions 9. Choice shift and group polarization Part III. Linkages with Other Formal Theories: 10. Models of group decision making 11. Expectation states and affect control 12. Individuals in groups Epilogue Appendices.
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attitude change affect control and expectation states in the formation of Influence Networks
2003Co-Authors: Noah E Friedkin, Eugene C JohnsenAbstract:This paper works at the intersections of affect control theory, expectation states theory, and social Influence Network theory. First, we introduce social Influence Network theory into affect control theory. We show how an Influence Network may emerge from the pattern of interpersonal sentiments in a group and how the fundamental sentiments that are at the core of affect control theory (dealing with the evaluation, potency, and activity of self and others) may be modified by interpersonal Influences. Second, we bring affect control theory and social Influence Network theory to bear on expectation states theory. In a task-oriented group, where persons’ performance expectations may be a major basis of their interpersonal Influence, we argue that persons’ fundamental sentiments may mediate effects of status characteristics on group members’ performance expectations. Based on the linkage of fundamental sentiments and interpersonal Influence, we develop an account of the formation of Influence Networks in groups that is applicable to both status homogeneous and status heterogeneous groups of any size, whether or not they are completely connected, and that is not restricted in scope to task-oriented groups.
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Social positions in Influence Networks
Social Networks, 1997Co-Authors: Noah E Friedkin, Eugene C JohnsenAbstract:In this article we derive implications about social positions from a formal theory of social Influence. The formal theory describes how, in a group of actors with heterogeneous initial opinions, a Network of interpersonal Influences enters into the formation of actors' settled opinions. We derive the following conclusions about a special form of structural equivalence. If actors are structurally equivalent in the Network of interpersonal Influences, then any dissimilarity of their initial opinions is reduced by the social Influence process. If the social positions of actors are identical, i.e. if they have identical initial opinions and are structurally equivalent in the Influence Network, then they have identical opinions at equilibrium. If actors are not structurally equivalent in the Network of interpersonal Influences, then the social Influence process does not necessarily reduce dissimilarities of initial opinions. We extend our analysis to consider automorphic equivalence.
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Social Influence Network Theory: Group Dynamics: Structural Social Psychology
Social Influence Network Theory, 1Co-Authors: Noah E Friedkin, Eugene C JohnsenAbstract:In this chapter, we present an overview of the group dynamics tradition that is our substantive focus, and we present our case for the advancement of this tradition via analysis of the attitude change process that unfolds in interpersonal Influence Networks. The idea that motivates this book is that some of the important lines of work on attitude change in small groups developed by psychologists (e.g., their work on social comparison, minority–majority factions, group polarization and choice shifts, and group decision schemes on attitudes) may be advanced if a social Network perspective is brought to bear on them. In addition, we show how certain lines of current work in sociological social psychology may be advanced with our approach. Sociologists are more likely to pursue these advances than psychologists, given the current emphasis in psychology on social cognition. However, as we emphasize, the Influence Network and process specified by our theory are a social cognition structure and process. Thus, we seek to move the two orientations into closer theoretical proximity and to build a theoretical interface that speaks to both psychological and sociological social psychologists. By attending to the classic foundations of modern social psychology, to the theoretical perspectives, hypotheses, and findings that constituted the group dynamics tradition, we hope to advance current work on small group social structures and social processes. We revisit the classical past, pursuing an agenda of formal unification, in order to reshape perspectives and trigger new research.
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Social Influence Network Theory: Minority and Majority Factions
Social Influence Network Theory, 1Co-Authors: Noah E Friedkin, Eugene C JohnsenAbstract:Few studies on social Influence have had the enduring impact of Asch's (1951; 1952; 1956) experiments on the conformity responses of individuals to a fixed unanimous majority. Asch's seminal investigation stimulated numerous studies, including work on the reverse situation – responses of a majority to a fixed minority position on an issue. A common theme in social Influence research has been the power of large versus small factions (though for counterexamples, see Moscovici, 1976; Nemeth, 1986). Many recent models of social Influence, such as social impact theory (Latane, 1981; Latane and Wolfe, 1981), the other–total ratio (Mullen, 1983), and the social Influence model (Tanford & Penrod, 1984) all use faction size as the central component. Research specifically focused on Influence in small groups has demonstrated the power of larger versus smaller factions (e.g., Tindale, Davis, Vollrath, Nagao, & Hinsz, 1990), and majority/plurality and related faction-size models have often been found to provide excellent fits to empirical data (e.g., Davis, 1982; Hastie, Penrod, & Pennington, 1983; Tindale & Davis, 1983, 1985)….Thus, for many small decision-making groups, a majority or faction-size model of social Influence in groups should provide a good baseline prediction (Tindale, et al. 1996: 81–2). It is now widely recognized that minority factions, including a minority of one confronting a unanimous faction of n − 1 others, may be influential. In particular, the work of Moscovici and his colleagues (Moscovici 1985; Moscovici and Mugny 1983; Mugny 1982; Nemeth 1986) on small factions, although controversial, has driven home the point that the Influence of persons who are not members of the majority faction also must be considered in any broad theory of group processes.
Raquel Ureña - One of the best experts on this subject based on the ideXlab platform.
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Trust based group decision making in environments with extreme uncertainty
Knowledge-Based Systems, 2020Co-Authors: Atefeh Taghavi, Esfandiar Eslami, Enrique Herrera-viedma, Raquel UreñaAbstract:In group decision making scenarios, where multiple anonymous agents interact, as is the case of social Networks, the uncertainty in the provided information as well as the diversity in the experts' opinions make of them a real challenge from the point of view of information aggregation and consensus achievement. This contribution addresses these two main issues in the following way: On the one hand, in order to deal with highly uncertainty group decision making scenarios, whose main particularity is that some of their experts may not be able to provide any single judgment about an alternative, the proposed approach estimates these missing information using the preferences coming from other trusted similar experts who present high degrees of confidence and consistency. On the other hand, with the objective of increasing the consensus among the agents involved in the decision making process, a feedback based Influence Network has been proposed. In this Network, the Influence between the agents is calculated by means of a dynamic combination of the inter agents trust, their self confidence, and their similarity. Thanks to this Influence Network our approach is able to recognize and isolate malicious users adjusting their Influence according to the trust degree between them.