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16
On Krause’s MultiAgent Consensus Model With StateDependent Connectivity
"... Abstract—We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than one. We give a new proof of convergence into clusters of agents, with all agents i ..."
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Cited by 58 (9 self)
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Abstract—We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than one. We give a new proof of convergence into clusters of agents, with all agents in the same cluster holding the same opinion. We then introduce a particular notion of equilibrium stability and provide lower bounds on the intercluster distances at a stable equilibrium. To better understand the behavior of the system when the number of agents is large, we also introduce and study a variant involving a continuum of agents, obtaining partial convergence results and lower bounds on intercluster distances, under some mild assumptions. Index Terms—Consensus, decentralized control, multiagent system, opinion dynamics.
Opinion dynamics in heterogeneous networks: convergence conjectures and theorems
 SIAM Journal on Control and Optimization
, 2012
"... Abstract. Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors ’ opinions. The neighbors of each agent can be defined as either (1) those agent ..."
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Abstract. Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors ’ opinions. The neighbors of each agent can be defined as either (1) those agents whose opinions are in its “confidence range, ” or (2) those agents whose “influence range” contain the agent’s opinion. The former definition is employed in Hegselmann and Krause’s bounded confidence model, and the latter is novel here. As the confidence and influence ranges are distinct for each agent, the heterogeneous statedependent interconnection topology leads to a poorlyunderstood complex dynamic behavior. In both models, we classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. Then, we define a positive invariant set centered at each equilibrium opinion vector. We show that if a trajectory enters one such set, then it converges to a steady state with constant interconnection topology. This result gives us a novel sufficient condition for both models to establish convergence, and is consistent with our conjecture that all trajectories of the bounded confidence and influence models eventually converge to a steady state under fixed topology.
Bayesian Updating Rules in Continuous Opinion Dynamics Models
, 2008
"... In this article, I investigate the use of Bayesian updating rules applied to modeling social agents in the case of continuos opinions models. Given another agent statement about the continuous value of a variable x, we will see that interesting dynamics emerge when an agent assigns a likelihood to t ..."
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Cited by 6 (4 self)
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In this article, I investigate the use of Bayesian updating rules applied to modeling social agents in the case of continuos opinions models. Given another agent statement about the continuous value of a variable x, we will see that interesting dynamics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a Uniform distribution. This represents the idea the other agent might have no idea about what he is talking about. The effect of updating only the first moments of the distribution will be studied. and we will see that this generates results similar to those of the Bounded Confidence models. By also updating the second moment, several different opinions always survive in the long run. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.
Taking into Account the Variations of Neighbourhood Sizes in the MeanField Approximation of the Threshold Model on a Random Network
 Journal of Artificial Societies and Social Simulation
, 2007
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Cited by 3 (0 self)
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Order preservation in a generalized version of Krause’s opinion dynamics model
, 2008
"... Abstract. Krause’s model of opinion dynamics has recently been the object of several studies, partly because it is one of the simplest multiagent systems involving positiondependent changing topologies. In this model, agents have an opinion represented by a real number and they update it by averag ..."
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Abstract. Krause’s model of opinion dynamics has recently been the object of several studies, partly because it is one of the simplest multiagent systems involving positiondependent changing topologies. In this model, agents have an opinion represented by a real number and they update it by averaging those agent opinions distant from their opinion by less than a certain interaction radius. Some results obtained on this model rely on the fact that the opinion orders remain unchanged under iteration, a property that is consistent with the intuition in models with simultaneous updating on a fully connected communication topology. Several variations of this model have been proposed. We show that some natural variations are not order preserving and therefore cause potential problems with the theoretical analysis and the consistence with the intuition. We consider a generic version of Krause’s model parameterized by an “influence function ” that encapsulates most of the variations proposed in the literature. We then derive a necessary and sufficient condition on this function for the opinion order to be preserved. 1.
A KINETIC APPROACH FOR MULTIDIMENSIONAL OPINION FORMATION IN PRESENCE OF MEDIA
"... Abstract. In this paper, we deal with a kinetic model to describe the evolution of the opinion in a closed group with respect to a choice between multiple options, e.g. political parties, which takes into account two main mechanisms of opinion formation, namely the interaction between individuals ..."
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Abstract. In this paper, we deal with a kinetic model to describe the evolution of the opinion in a closed group with respect to a choice between multiple options, e.g. political parties, which takes into account two main mechanisms of opinion formation, namely the interaction between individuals and the eect of the mass media. We provide an existence and uniqueness result for the model, and then we numerically test it in some relevant cases. 1.
On Krause’s consensus multiagent model with statedependent connectivity (Extended version)
, 2009
"... We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than 1. We give a new proof of convergence into clusters of agents, with all agents in the same ..."
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We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than 1. We give a new proof of convergence into clusters of agents, with all agents in the same cluster holding the same opinion. We then introduce a particular notion of equilibrium stability and provide lower bounds on the intercluster distances at a stable equilibrium. To better understand the behavior of the system when the number of agents is large, we also introduce and study a variant involving a continuum of agents, obtaining partial convergence results and lower bounds on intercluster distances, under some mild assumptions.