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- DeGroot-based opinion formation under a global steering mechanism(arXiv)
Author : Ivan Conjeaud, Philipp Lorenz-Spreen, Argyris Kalogeratos
Abstract : This paper investigates how interacting agents arrive to a consensus or a polarized state. We study the opinion formation process under the effect of a global steering mechanism (GSM), which aggregates the opinion-driven stochastic agent states at the network level and feeds back to them a form of global information. We also propose a new two-layer agent-based opinion formation model, called GSM-DeGroot, that captures the coupled dynamics between agent-to-agent local interactions and the GSM’s steering effect. This way, agents are subject to the effects of a DeGroot-like local opinion propagation, as well as to a wide variety of possible aggregated information that can affect their opinions, such as trending news feeds, press coverage, polls, elections, etc. Contrary to the standard DeGroot model, our model allows polarization to emerge by letting agents react to the global information in a stubborn differential way. Moreover, the introduced stochastic agent states produce event stream dynamics that can fit to real event data. We explore numerically the model dynamics to find regimes of qualitatively different behavior. We also challenge our model by fitting it to the dynamics of real topics that attracted the public attention and were recorded on Twitter. Our experiments show that the proposed model holds explanatory power, as it evidently captures real opinion formation dynamics via a relatively small set of interpretable parameters.
2. Granular DeGroot Dynamics — a Model for Robust Naive Learning in Social Networks(arXiv)
Author : Gideon Amir, Itai Arieli, Galit Ashkenazi-Golan, Ron Peretz
Abstract : We study a model of opinion exchange in social networks where a state of the world is realized and every agent receives a zero-mean noisy signal of the realized state. It is known from [Golub and Jackson 2010] that under DeGroot dynamics [DeGroot 1974] agents reach a consensus that is close to the state of the world when the network is large. The DeGroot dynamics, however, is highly non-robust and the presence of a single “stubborn agent’’ that does not adhere to the updating rule can sway the public consensus to any other value. We introduce a variant of DeGroot dynamics that we call emph{ 1m-DeGroot}. 1m-DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with m as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, 1m-DeGroot dynamics is highly robust both to the presence of stubborn agents and to certain types of misspecifications