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Francesco Bullo - One of the best experts on this subject based on the ideXlab platform.
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Social power evolution in influence networks with stubborn individuals
IEEE Transactions on Automatic Control, 2021Co-Authors: Ye Tian, Noah E Friedkin, Anahita Mirtabatabaei, Peng Jia, Long Wang, Francesco BulloAbstract:This paper studies the evolution of social power in influence networks with stubborn individuals. Based on the Friedkin-Johnsen opinion dynamics and the Reflected Appraisal mechanism, two models are proposed over issue sequences and over a single issue, respectively. These models generalize the original DeGroot-Friedkin (DF) model by including stubbornness. To the best of our knowledge, this paper is the first attempt to investigate the social power evolution of stubborn individuals basing on the Reflected Appraisal mechanism. Properties of equilibria and convergence are provided. We show that the models have same equilibrium social power and convergence property, where the equilibrium social power depends only upon interpersonal influence and individuals' stubbornness. Roughly speaking, more stubborn individual has more equilibrium social power. Moreover, unlike the DF model without stubbornness, we prove that for the models with stubbornness, autocracy can never be achieved, while democracy can be achieved under any network topology.
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opinion dynamics and social power evolution a single timescale model
IEEE Transactions on Control of Network Systems, 2020Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:This article studies the evolution of self-Appraisal and social power in a social influence system. We consider a modification of the recent DeGroot–Friedkin (DF) model, called the single–timescale DF model, in which the opinion formation process takes place on the same timescale as the Reflected Appraisal process. We provide a comprehensive analysis of the equilibria and convergence properties of the model for the settings of irreducible and reducible influence networks. For the setting of irreducible influence networks, the single-timescale DF model has the same behavior as the original DF model, e.g., it predicts among other things that the social power ranking among individuals is asymptotically equal to their centrality ranking, and that social power tends to accumulate at the top of the centrality ranking hierarchy. For the setting of reducible influence networks, the single-timescale DF model behaves differently from the original DF model in ways that we fully characterize.
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opinion dynamics and social power evolution a single timescale model
arXiv: Optimization and Control, 2017Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:This paper studies the evolution of self-Appraisal and social power, for a group of individuals who discuss and form opinions. We consider a modification of the recently proposed DeGroot-Friedkin (DF) model, in which the opinion formation process takes place on the same timescale as the Reflected Appraisal process; we call this new model the single-timescale DF model. We provide a comprehensive analysis of the equilibria and convergence properties of the model for the settings of irreducible and reducible influence networks. For the setting of irreducible influence networks, the single-timescale DF model has the same behavior as the original DF model, that is, it predicts among other things 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 centrality ranking hierarchy, and that an autocratic (resp., democratic) power structure arises when the centrality scores are maximally nonuniform (resp., uniform). For the setting of reducible influence networks, the single-timescale DF model behaves differently from the original DF model in two ways. First, an individual, who corresponds to a reducible node in a reducible influence network, can keep all social power in the single-timescale DF model if the initial condition does so, whereas its social power asymptotically vanishes in the original DF model. Second, when the associated network has multiple sinks, the two models behave very differently: the original DF model has a single globally-attractive equilibrium, whereas any partition of social power among the sinks is allowable at equilibrium in the single-timescale DF model.
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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,...
Noah E Friedkin - One of the best experts on this subject based on the ideXlab platform.
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Social power evolution in influence networks with stubborn individuals
IEEE Transactions on Automatic Control, 2021Co-Authors: Ye Tian, Noah E Friedkin, Anahita Mirtabatabaei, Peng Jia, Long Wang, Francesco BulloAbstract:This paper studies the evolution of social power in influence networks with stubborn individuals. Based on the Friedkin-Johnsen opinion dynamics and the Reflected Appraisal mechanism, two models are proposed over issue sequences and over a single issue, respectively. These models generalize the original DeGroot-Friedkin (DF) model by including stubbornness. To the best of our knowledge, this paper is the first attempt to investigate the social power evolution of stubborn individuals basing on the Reflected Appraisal mechanism. Properties of equilibria and convergence are provided. We show that the models have same equilibrium social power and convergence property, where the equilibrium social power depends only upon interpersonal influence and individuals' stubbornness. Roughly speaking, more stubborn individual has more equilibrium social power. Moreover, unlike the DF model without stubbornness, we prove that for the models with stubbornness, autocracy can never be achieved, while democracy can be achieved under any network topology.
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opinion dynamics and social power evolution a single timescale model
IEEE Transactions on Control of Network Systems, 2020Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:This article studies the evolution of self-Appraisal and social power in a social influence system. We consider a modification of the recent DeGroot–Friedkin (DF) model, called the single–timescale DF model, in which the opinion formation process takes place on the same timescale as the Reflected Appraisal process. We provide a comprehensive analysis of the equilibria and convergence properties of the model for the settings of irreducible and reducible influence networks. For the setting of irreducible influence networks, the single-timescale DF model has the same behavior as the original DF model, e.g., it predicts among other things that the social power ranking among individuals is asymptotically equal to their centrality ranking, and that social power tends to accumulate at the top of the centrality ranking hierarchy. For the setting of reducible influence networks, the single-timescale DF model behaves differently from the original DF model in ways that we fully characterize.
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opinion dynamics and social power evolution a single timescale model
arXiv: Optimization and Control, 2017Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:This paper studies the evolution of self-Appraisal and social power, for a group of individuals who discuss and form opinions. We consider a modification of the recently proposed DeGroot-Friedkin (DF) model, in which the opinion formation process takes place on the same timescale as the Reflected Appraisal process; we call this new model the single-timescale DF model. We provide a comprehensive analysis of the equilibria and convergence properties of the model for the settings of irreducible and reducible influence networks. For the setting of irreducible influence networks, the single-timescale DF model has the same behavior as the original DF model, that is, it predicts among other things 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 centrality ranking hierarchy, and that an autocratic (resp., democratic) power structure arises when the centrality scores are maximally nonuniform (resp., uniform). For the setting of reducible influence networks, the single-timescale DF model behaves differently from the original DF model in two ways. First, an individual, who corresponds to a reducible node in a reducible influence network, can keep all social power in the single-timescale DF model if the initial condition does so, whereas its social power asymptotically vanishes in the original DF model. Second, when the associated network has multiple sinks, the two models behave very differently: the original DF model has a single globally-attractive equilibrium, whereas any partition of social power among the sinks is allowable at equilibrium in the single-timescale DF model.
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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,...
Peng Jia - One of the best experts on this subject based on the ideXlab platform.
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Social power evolution in influence networks with stubborn individuals
IEEE Transactions on Automatic Control, 2021Co-Authors: Ye Tian, Noah E Friedkin, Anahita Mirtabatabaei, Peng Jia, Long Wang, Francesco BulloAbstract:This paper studies the evolution of social power in influence networks with stubborn individuals. Based on the Friedkin-Johnsen opinion dynamics and the Reflected Appraisal mechanism, two models are proposed over issue sequences and over a single issue, respectively. These models generalize the original DeGroot-Friedkin (DF) model by including stubbornness. To the best of our knowledge, this paper is the first attempt to investigate the social power evolution of stubborn individuals basing on the Reflected Appraisal mechanism. Properties of equilibria and convergence are provided. We show that the models have same equilibrium social power and convergence property, where the equilibrium social power depends only upon interpersonal influence and individuals' stubbornness. Roughly speaking, more stubborn individual has more equilibrium social power. Moreover, unlike the DF model without stubbornness, we prove that for the models with stubbornness, autocracy can never be achieved, while democracy can be achieved under any network topology.
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opinion dynamics and social power evolution a single timescale model
IEEE Transactions on Control of Network Systems, 2020Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:This article studies the evolution of self-Appraisal and social power in a social influence system. We consider a modification of the recent DeGroot–Friedkin (DF) model, called the single–timescale DF model, in which the opinion formation process takes place on the same timescale as the Reflected Appraisal process. We provide a comprehensive analysis of the equilibria and convergence properties of the model for the settings of irreducible and reducible influence networks. For the setting of irreducible influence networks, the single-timescale DF model has the same behavior as the original DF model, e.g., it predicts among other things that the social power ranking among individuals is asymptotically equal to their centrality ranking, and that social power tends to accumulate at the top of the centrality ranking hierarchy. For the setting of reducible influence networks, the single-timescale DF model behaves differently from the original DF model in ways that we fully characterize.
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opinion dynamics and social power evolution a single timescale model
arXiv: Optimization and Control, 2017Co-Authors: Peng Jia, Noah E Friedkin, Francesco BulloAbstract:This paper studies the evolution of self-Appraisal and social power, for a group of individuals who discuss and form opinions. We consider a modification of the recently proposed DeGroot-Friedkin (DF) model, in which the opinion formation process takes place on the same timescale as the Reflected Appraisal process; we call this new model the single-timescale DF model. We provide a comprehensive analysis of the equilibria and convergence properties of the model for the settings of irreducible and reducible influence networks. For the setting of irreducible influence networks, the single-timescale DF model has the same behavior as the original DF model, that is, it predicts among other things 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 centrality ranking hierarchy, and that an autocratic (resp., democratic) power structure arises when the centrality scores are maximally nonuniform (resp., uniform). For the setting of reducible influence networks, the single-timescale DF model behaves differently from the original DF model in two ways. First, an individual, who corresponds to a reducible node in a reducible influence network, can keep all social power in the single-timescale DF model if the initial condition does so, whereas its social power asymptotically vanishes in the original DF model. Second, when the associated network has multiple sinks, the two models behave very differently: the original DF model has a single globally-attractive equilibrium, whereas any partition of social power among the sinks is allowable at equilibrium in the single-timescale DF model.
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on the dynamics of influence networks via Reflected Appraisal
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.
Anahita Mirtabatabaei - One of the best experts on this subject based on the ideXlab platform.
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Social power evolution in influence networks with stubborn individuals
IEEE Transactions on Automatic Control, 2021Co-Authors: Ye Tian, Noah E Friedkin, Anahita Mirtabatabaei, Peng Jia, Long Wang, Francesco BulloAbstract:This paper studies the evolution of social power in influence networks with stubborn individuals. Based on the Friedkin-Johnsen opinion dynamics and the Reflected Appraisal mechanism, two models are proposed over issue sequences and over a single issue, respectively. These models generalize the original DeGroot-Friedkin (DF) model by including stubbornness. To the best of our knowledge, this paper is the first attempt to investigate the social power evolution of stubborn individuals basing on the Reflected Appraisal mechanism. Properties of equilibria and convergence are provided. We show that the models have same equilibrium social power and convergence property, where the equilibrium social power depends only upon interpersonal influence and individuals' stubbornness. Roughly speaking, more stubborn individual has more equilibrium social power. Moreover, unlike the DF model without stubbornness, we prove that for the models with stubbornness, autocracy can never be achieved, while democracy can be achieved under any network topology.
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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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on the dynamics of influence networks via Reflected Appraisal
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.
Tamer Basar - One of the best experts on this subject based on the ideXlab platform.
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on convergence rate of a continuous time distributed self Appraisal model with time varying relative interaction matrices
Conference on Decision and Control, 2017Co-Authors: Tamer BasarAbstract:This paper studies a recently proposed continuous-time distributed self-Appraisal model with time-varying interactions among a network of n individuals which are characterized by a sequence of time-varying relative interaction matrices. The model describes the evolution of the social-confidence levels of the individuals via a Reflected Appraisal mechanism in real time. We show that when the relative interaction matrices are doubly stochastic, the n individuals' self-confidence levels will all converge to 1/n, which indicates a democratic state, exponentially fast under appropriate assumptions, and provide an explicit expression for the convergence rate. Numerical examples are provided to verify the theoretical results and to show that when the relative interaction matrices are stochastic (not doubly stochastic), the social-confidence levels of the individuals may not converge to a steady state.
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on convergence rate of a continuous time distributed self Appraisal model with time varying relative interaction matrices
arXiv: Optimization and Control, 2017Co-Authors: Tamer BasarAbstract:This paper studies a recently proposed continuous-time distributed self-Appraisal model with time-varying interactions among a network of $n$ individuals which are characterized by a sequence of time-varying relative interaction matrices. The model describes the evolution of the social-confidence levels of the individuals via a Reflected Appraisal mechanism in real time. We first show by example that when the relative interaction matrices are stochastic (not doubly stochastic), the social-confidence levels of the individuals may not converge to a steady state. We then show that when the relative interaction matrices are doubly stochastic, the $n$ individuals' self-confidence levels will all converge to $1/n$, which indicates a democratic state, exponentially fast under appropriate assumptions, and provide an explicit expression of the convergence rate.
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on a modified degroot friedkin model of opinion dynamics
Advances in Computing and Communications, 2015Co-Authors: Ji Liu, Tamer BasarAbstract:This paper studies the opinion dynamics that result when individuals consecutively discuss a sequence of issues. Specifically, we study how individuals' self-confidence levels evolve via a Reflected Appraisal mechanism. Motivated by the DeGroot-Friedkin model, we propose a Modified DeGroot-Friedkin model which allows individuals to update their self-confidence levels by only interacting with their neighbors and in particular, the modified model allows the update of self-confidence levels to take place in finite time without waiting for the opinion process to reach a consensus on any particular issue. We study properties of this Modified DeGroot-Friedkin model and compare the associated equilibria and stability with those of the original DeGroot-Friedkin model. Specifically, for the case when the interaction matrix is doubly stochastic, we show that for the modified model, the vector of individuals' self-confidence levels converges to a unique nontrivial equilibrium which for each individual is equal to 1 over n, where n is the number of individuals. This implies that eventually individuals reach a democratic state.
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on a modified degroot friedkin model of opinion dynamics
arXiv: Optimization and Control, 2015Co-Authors: Ji Liu, Tamer BasarAbstract:This paper studies the opinion dynamics that result when individuals consecutively discuss a sequence of issues. Specifically, we study how individuals' self-confidence levels evolve via a Reflected Appraisal mechanism. Motivated by the DeGroot-Friedkin model, we propose a Modified DeGroot-Friedkin model which allows individuals to update their self-confidence levels by only interacting with their neighbors and in particular, the modified model allows the update of self-confidence levels to take place in finite time without waiting for the opinion process to reach a consensus on any particular issue. We study properties of this Modified DeGroot-Friedkin model and compare the associated equilibria and stability with those of the original DeGroot-Friedkin model. Specifically, for the case when the interaction matrix is doubly stochastic, we show that for the modified model, the vector of individuals' self-confidence levels asymptotically converges to a unique nontrivial equilibrium which for each individual is equal to 1/n, where n is the number of individuals. This implies that eventually, individuals reach a democratic state.