We study generalizations of the Hegselmann-Krause (HK) model for opinion dynamics, incorporating features and parameters that are natural components of observed social systems. The first generalization is one where the strength of influence depends on the distance of the agents' opinions. Under this setup, we identify conditions under which the opinions converge in finite time, and provide a qualitative characterization of the equilibrium. We interpret the HK model opinion update rule as a quadratic cost-minimization rule. This enables a second generalization: a family of update rules which possess different equilibrium properties. Subsequently, we investigate models in which a external force can behave strategically to modulate influence user updates. We consider cases where this external force can introduce additional agents and cases where they can modify the cost structures for other agents. We describe and analyze some strategies through which such modulation may be possible in an order-optimal manner. Our simulations demonstrate that generalized dynamics differ qualitatively and quantitatively from traditional HK dynamics.
Models for opinion dynamics have been studied in a variety of fields, including sociology, physics, computer science, and engineering. The wide range of models @cite_5 can be divided into two broad approaches: dynamical systems and agent-based modeling. Agent-based models in which each social element or entity acts based on actions or positions of others have been studied extensively. Agents take actions to pursue an objective such as social welfare maximization, individual benefit, or learning @cite_9 @cite_21 @cite_11 @cite_17 .
@cite_11 @cite_9 @cite_21 @cite_5 @cite_17
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Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines such as physics, mathematics, computer science, social psychology and philosophy. In these models agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agent-based simulations in a Monte Carlo style, but they can also be reformulated on the agent's density in the opinion space in a master equation style. The contribution of this survey is fourfold. First, it will present the agent-based and density-based modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds o... Krause’s model of opinion dynamics has recently been the subject of several studies, partly because it is one of the simplest multi-agent systems involving position-dependent 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. As a key sub-field of social dynamics and sociophysics, opinion dynamics utilizes mathematical and physical models and the agent-based computational modeling tools, to investigate the spreading of opinions in a collection of human beings. This research field stems from various disciplines in social sciences, especially the social influence models developed in social psychology and sociology. A multidisciplinary review is given in this paper, attempting to keep track of the historical development of the field and to shed light on its future directions. In the review, the authors discuss the disciplinary origins of opinion dynamics, showing that the combination of the social processes, which are conventionally studied in social sciences, and the analytical and computational tools, which are developed in mathematics, physics and complex system studies, gives birth to the interdisciplinary field of opinion dynamics. The current state of the art of opinion dynamics is then overviewed, with the research progresses on the typical models like the voter model, the Sznajd model, the culture dissemination model, and the bounded confidence model being highlighted. Correspondingly, the future directions of this academic field are envisioned, with an advocation for closer synthesis of the related disciplines. We present an introduction to a novel model of an individual and group opinion dynamics, taking into account different ways in which different sources of information are filtered due to cognitive biases. The agent based model, using Bayesian updating of the individual belief distribution, is based on the recent psychology work by Dan Kahan. Open nature of the model allows to study the effects of both static and time-dependent biases and information processing filters. In particular, the paper compares the effects of two important psychological mechanisms: the confirmation bias and the politically motivated reasoning. Depending on the effectiveness of the information filtering (agent bias), the agents confronted with an objective information source may either reach a consensus based on the truth, or remain divided despite the evidence. In general, the model might provide an understanding into the increasingly polarized modern societies, especially as it allows mixing of different types of filters: psychological, social, and algorithmic.