Binary Opinion Dynamics with Stubborn Agents
01 Dec 2013-Vol. 1, Iss: 4, pp 19
TL;DR: It is shown that the presence of stubborn agents with opposing opinions precludes convergence to consensus; instead, opinions converge in distribution with disagreement and fluctuations.
Abstract: We study binary opinion dynamics in a social network with stubborn agents who influence others but do not change their opinions. We focus on a generalization of the classical voter model by introducing nodes (stubborn agents) that have a fixed state. We show that the presence of stubborn agents with opposing opinions precludes convergence to consensus; instead, opinions converge in distribution with disagreement and fluctuations. In addition to the first moment of this distribution typically studied in the literature, we study the behavior of the second moment in terms of network properties and the opinions and locations of stubborn agents. We also study the problem of optimal placement of stubborn agents where the location of a fixed number of stubborn agents is chosen to have the maximum impact on the long-run expected opinions of agents.
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TL;DR: The aim of this tutorial is to highlight a novel chapter of control theory, dealing with applications to social systems, to the attention of the broad research community.
382 citations
TL;DR: A review of the framework and formulation of opinion dynamics as well as some basic models, extensions, and applications are presented and several open problems are proposed for future research.
253 citations
TL;DR: The problem of coordination and control of social systems is the foundational problem of sociology as discussed by the authors, which was established in Europe in the aftermath of the American and French Revolutions and became a preoccupation.
Abstract: The coordination and control of social systems is the foundational problem of sociology. The discipline was established in Europe in the aftermath of the American and French Revolutions. With the dismantling of the hierarchical controls of European aristocratic systems, the examination of alternative mechanisms of coordination and control became a preoccupation. The Industrial Revolution (c. 1760-1840), which was occurring at the same time, reinforced this preoccupation by decoupling the power of purse and the power of positions of authority. While the hierarchies of church and state retained coercive power, the exercise of such power was increasingly contested. The moral compass of society, its general welfare, and its capacity to adapt to changing circumstances appeared to be aggregated properties of the unconstrained opinions and behaviors of a large collectivity of individuals. The definition of the problem of coordination and control, which emerged in Europe in the new discipline of sociology, still resonates and guides current sociological work. The problem definition [1], broadly stated, is this: if value is placed on nonhierarchical mechanisms of social control, then what mechanisms and structures (consistent with this value) allow a coordination and control of social systems?
188 citations
TL;DR: In this paper, the authors investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks).
Abstract: We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental limitations on the performance of any distributed optimization algorithm in the presence of adversaries. We then propose a secure distributed optimization algorithm that guarantees that the nonadversarial nodes converge to the convex hull of the minimizers of their local functions under the certain conditions on the graph topology, regardless of the actions of a certain number of the adversarial nodes. In particular, we provide sufficient conditions on the graph topology to tolerate a bounded number of adversaries in the neighborhood of every nonadversarial node, and necessary and sufficient conditions to tolerate a globally bounded number of adversaries. For situations, where there are up to $F$ adversaries in the neighborhood of every node, we use the concept of maximal $F$ -local sets of graphs to provide lower bounds on the distance-to-optimality of achievable solutions under any algorithm. We show that finding the size of such sets is NP-hard.
176 citations
TL;DR: In this paper, the authors highlight a novel chapter of control theory, dealing with dynamic models of social networks and processes over them, to the attention of the broad research community, and focus on more recent models of complex networks that have been developed concurrently with MAS theory.
Abstract: Recent years have witnessed a significant trend towards filling the gap between Social Network Analysis (SNA) and control theory. This trend was enabled by the introduction of new mathematical models describing dynamics of social groups, the development of algorithms and software for data analysis and the tremendous progress in understanding complex networks and multi-agent systems (MAS) dynamics. The aim of this tutorial is to highlight a novel chapter of control theory, dealing with dynamic models of social networks and processes over them, to the attention of the broad research community. In its first part [1], we have considered the most classical models of social dynamics, which have anticipated and to a great extent inspired the recent extensive studies on MAS and complex networks. This paper is the second part of the tutorial, and it is focused on more recent models of social processes that have been developed concurrently with MAS theory. Future perspectives of control in social and techno-social systems are also discussed.
176 citations
References
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TL;DR: In this article, the authors analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision, and they show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior.
Abstract: We analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision. This is rational for her because these other decision makers may have some information that is important for her. We then show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior; i.e., people will be doing what others are doing rather than using their information. We then show that the resulting equilibrium is inefficient.
5,956 citations
24 Aug 2003
TL;DR: An analysis framework based on submodular functions shows that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models, and suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.
Abstract: Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.
5,887 citations
TL;DR: A growth model for the timing of initial purchase of new products is developed and tested empirically against data for eleven consumer durables, and a long-range forecast is developed for the sales of color television sets.
Abstract: (This article originally appeared in Management Science, January 1969, Volume 15, Number 5, pp. 215-227, published by The Institute of Management Sciences.)
A growth model for the timing of initial purchase of new products is developed and tested empirically against data for eleven consumer durables. The basic assumption of the model is that the timing of a consumer's initial purchase is related to the number of previous buyers. A behavioral rationale for the model is offered in terms of innovative and imitative behavior. The model yields good predictions of the sales peak and the timing of the peak when applied to historical data. A long-range forecast is developed for the sales of color television sets.
4,734 citations
TL;DR: The problem of finding the most influential nodes in a social network is NP-hard as mentioned in this paper, and the first provable approximation guarantees for efficient algorithms were provided by Domingos et al. using an analysis framework based on submodular functions.
Abstract: Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.
4,390 citations
Book•
31 Dec 1985
TL;DR: The construction, and other general results are given in this paper, with values in [0, ] s. The voter model, the contact process, the nearest-particle system, and the exclusion process.
Abstract: The Construction, and Other General Results.- Some Basic Tools.- Spin Systems.- Stochastic Ising Models.- The Voter Model.- The Contact Process.- Nearest-Particle Systems.- The Exclusion Process.- Linear Systems with Values in [0, ?)s.
4,365 citations