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Spread of (mis)information in social networks
, 2009
"... We provide a model to investigate the tension between information aggregation and spread of misinformation in large societies (conceptualized as networks of agents communicating with each other). Each individual holds a belief represented by a scalar. Individuals meet pairwise and exchange informati ..."
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Cited by 43 (7 self)
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We provide a model to investigate the tension between information aggregation and spread of misinformation in large societies (conceptualized as networks of agents communicating with each other). Each individual holds a belief represented by a scalar. Individuals meet pairwise and exchange information, which is modeled as both individuals adopting the average of their pre-meeting beliefs. When all individuals engage in this type of information exchange, the society will be able to effectively aggregate the initial information held by all individuals. There is also the possibility of misinformation, however, because some of the individuals are “forceful, ” meaning that they influence the beliefs of (some) of the other individuals they meet, but do not change their own opinion. The paper characterizes how the presence of forceful agents interferes with information aggregation. Under the assumption that even forceful agents obtain some information (however infrequent) from some others (and additional weak regularity conditions), we first show that beliefs in this class of societies converge to a consensus among all individuals. This consensus value is a random variable, however, and we characterize its behavior. Our main results quantify the extent of misinformation in the society by either providing bounds or exact results (in some special cases) on how far the consensus value can be from the benchmark without forceful agents (where there is efficient information aggregation). The worst outcomes obtain when there are several forceful agents and forceful agents themselves update their beliefs only on the basis of information they obtain from individuals most likely to have received their own information previously.
OPINION FLUCTUATIONS AND DISAGREEMENT IN SOCIAL NETWORKS
- SUBMITTED TO THE ANNALS OF APPLIED PROBABILITY
, 2010
"... We study a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent ..."
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Cited by 26 (5 self)
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We study a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent leaders, political parties or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, opinion dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society almost surely fail to converge, and the belief of each regular agent converges in law to a non-degenerate random variable. The model thus generates longrun disagreement and continuous opinion fluctuations. The structure of the social network and the location of stubborn agents within it shape opinion dynamics. When the society is “highly fluid”, meaning that the mixing time of the random walk on the graph describing the social network is small relative to (the inverse of) the relative size of the linkages to stubborn agents, the ergodic beliefs of most of the agents concentrate around a certain common value. We also show that under additional conditions, the ergodic beliefs distribution becomes “approximately chaotic”, meaning that the variance of the aggregate belief of the society vanishes in the large population limit while individual opinions still fluctuate significantly.
Discrete Opinion Dynamics with Stubborn Agents
"... We study discrete opinion dynamics in a social network with ”stubborn agents” who influence others but do not change their opinions. We generalize the classical voter model by introducing nodes (stubborn agents) that have a fixed state. We show that the presence of stubborn agents with opposing opin ..."
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Cited by 18 (1 self)
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We study discrete opinion dynamics in a social network with ”stubborn agents” who influence others but do not change their opinions. We generalize 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.
Opinion fluctuations and persistent disagreement in social networks
- in Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on. IEEE, 2011
"... Abstract — Disagreement among individuals in a society, even on central questions that have been debated for centuries, is the rule; agreement is the rare exception. How can disagreement of this sort persist for so long? Most existing models of com-munication and learning, based on Bayesian or non-B ..."
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Cited by 15 (1 self)
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Abstract — Disagreement among individuals in a society, even on central questions that have been debated for centuries, is the rule; agreement is the rare exception. How can disagreement of this sort persist for so long? Most existing models of com-munication and learning, based on Bayesian or non-Bayesian updating mechanisms, typically lead to consensus provided that communication takes place over a strongly connected network. These models are thus unable to explain persistent disagreements, and belief fluctuations. We propose a tractable model that generates long-run disagree-ments and persistent opinion fluctuations. Our model involves a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent leaders, political parties or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, the belief dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society almost surely fail to converge, the belief profile keeps on oscillating in an ergodic fashion, and it converges in law to a non-degenerate random vector. The structure of the graph describing the social network and the location of stubborn agents within it shape the long run behavior of the opinion dynamics. We prove that, when the society is highly fluid, meaning that the mixing time of the random walk on the graph describing the social network is small relative to the inverse of the relative size of the linkages to stubborn agents, a condition of homogeneous influence emerges, whereby the ergodic beliefs of most of the regular agents have approximately equal marginal distributions. This clearly need not imply approximate consensus and in fact we show, under mild conditions, the ergodic belief distribution becomes approximately chaotic, meaning that the variance of the aggregate belief of the society vanishes in the large population limit while individual opinions still fluctuate significantly in an essentially uncorrelated way. I.
Efficient bayesian learning in social networks with gaussian estimators
, 2010
"... We propose a Bayesian model of iterative learning on social networks that is computationally tractable; the agents of this model are fully rational, and their calculations can be performed with modest computational resources for large networks. Furthermore, learning is efficient, in the sense that t ..."
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Cited by 10 (3 self)
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We propose a Bayesian model of iterative learning on social networks that is computationally tractable; the agents of this model are fully rational, and their calculations can be performed with modest computational resources for large networks. Furthermore, learning is efficient, in the sense that the process results in an information-theoretically optimal belief. This result extends Condorcet’s Jury Theorem to general social networks, preserving rationality, computational feasibility and efficient learning. The model consists of a group of agents who belong to a social network, so that a pair of agents can observe each other’s actions only if they are neighbors. We assume that the network is connected and that the agents have full knowledge of the structure of the network, so that they know the members of the network and their social connections. The agents try to estimate some state of the world S (say, the price of oil a year from today). Each agent has a private measurement: an independently acquired piece of information regarding S. This is modeled, for agent v, by a number Sv picked from a Gaussian distribution with mean S and standard deviation one. Accordingly, agent v’s prior belief regarding S is a normal distribution with mean Sv and standard deviation one. The agents start acting iteratively. At each iteration, each agent takes the optimal action given its current belief. This action reveals its mean estimate of S to its neighbors. Then, observing its neighbors ’ actions, each agent updates its belief, using Bayes ’ Law. We show that this process is efficient: all the agents converge to the belief that they would have, had they access to all the private measurements. Additionally, and in contrast to other iterative Bayesian models on networks, it is computationally efficient, so that each agent’s calculation can be easily carried out.
Influential listeners: An experiment on persuasion bias in social networks
- European Economic Review
"... This paper presents an experimental investigation of persuasion bias, a form of bounded rationality whereby agents communicating through a social network are unable to account for possible repetitions in the information they receive. The results indicate that network structure plays a significant ro ..."
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Cited by 9 (1 self)
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This paper presents an experimental investigation of persuasion bias, a form of bounded rationality whereby agents communicating through a social network are unable to account for possible repetitions in the information they receive. The results indicate that network structure plays a significant role in determining social influence. How-ever, the most influential agents are not those with more outgoing links, as predicted by the persuasion bias hypothesis, but those with more incoming links. We show that a boundedly rational updating rule that takes into account not only agents ' outdegree, but also their inde-gree, provides a better explanation of the experimental data. In this framework, consensus beliefs tend to be swayed towards the opinions of influential listeners. We then present an effort-weighted updating model as a more general characterization of information aggregation in social networks.
Convergence of Rule-of-Thumb Learning Rules in Social Networks
"... Abstract — We study the problem of dynamic learning by a social network of agents. Each agent receives a signal about an underlying state and communicates with a subset of agents (his neighbors) in each period. The network is connected. In contrast to the majority of existing learning models, we foc ..."
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Cited by 8 (0 self)
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Abstract — We study the problem of dynamic learning by a social network of agents. Each agent receives a signal about an underlying state and communicates with a subset of agents (his neighbors) in each period. The network is connected. In contrast to the majority of existing learning models, we focus on the case where the underlying state is time-varying. We consider the following class of rule of thumb learning rules: at each period, each agent constructs his posterior as a weighted average of his prior, his signal and the information he receives from neighbors. The weights given to signals can vary over time and the weights given to neighbors can vary across agents. We distinguish between two subclasses: (1) constant weight rules; (2) diminishing weight rules. The latter reduces weights given to signals asymptotically to 0. Our main results characterize the asymptotic behavior of beliefs. We show that the general class of rules leads to unbiased estimates of the underlying state. When the underlying state has innovations with variance tending to zero asymptotically, we show that the diminishing weight rules ensure convergence in the mean-square sense. In contrast, when the underlying state has persistent innovations, constant weight rules enable us to characterize explicit bounds on the mean square error between an agent’s belief and the underlying state as a function of the type of learning rule and signal structure. I.
The Dynamics of Influence Systems
, 2012
"... Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while Turing-complete, influence dynamics of the diffusive type is almost surely as ..."
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Cited by 6 (4 self)
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Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while Turing-complete, influence dynamics of the diffusive type is almost surely asymptotically periodic. Besides resolving the dynamics of a popular family of multiagent systems, the other contribution of this work is to introduce a new type of renormalization-based bifurcation analysis for multiagent systems.
Monopoly Pricing in the Presence of Social Learning
, 2011
"... To be submitted on November 2011 A monopolist offers a product to a market of consumers with heterogeneous quality preferences. Although initially uninformed about the product quality, they learn by observing past purchase decisions and reviews of other consumers. Our goal is to analyze the social l ..."
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Cited by 6 (0 self)
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To be submitted on November 2011 A monopolist offers a product to a market of consumers with heterogeneous quality preferences. Although initially uninformed about the product quality, they learn by observing past purchase decisions and reviews of other consumers. Our goal is to analyze the social learning mechanism and its effect on the seller’s pricing decision. This analysis borrows from the literature on social learning and on pricing and revenue management. Consumers follow a naive decision rule and, under some conditions, eventually learn the product’s quality. Using mean-field approximation, the dynamics of this learning process are characterized for markets with high demand intensity. The relationship between the price and the speed of learning depends on the heterogeneity of quality preferences. Two pricing strategies are studied: a static price and a single price change. Properties of the optimal prices are derived. Numerical experiments suggest that pricing strategies that account for social learning may increase revenues considerably relative to strategies that do not.
Chinese Restaurant Game
"... Abstract—In this letter, by introducing the strategic decision making into the Chinese restaurant process, we propose a new game, called Chinese Restaurant Game, as a new general framework for analyzing the individual decision problem in a network with negative network externality. Our analysis show ..."
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Cited by 6 (4 self)
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Abstract—In this letter, by introducing the strategic decision making into the Chinese restaurant process, we propose a new game, called Chinese Restaurant Game, as a new general framework for analyzing the individual decision problem in a network with negative network externality. Our analysis shows that a balance in utilities among the customers in the game will eventually be achieved under the strategic decision making process. The equilibrium grouping is defined to describe the predicted outcome of the proposed game, which can be found by a simple algorithm. The simulation results confirm that the rational customers in Chinese restaurant game automatically achieve a balance in loading in order to reduce the impact from the negative network externality. Index Terms—Chinese restaurant game, game theory, Nash equilibrium, network externality. I.
