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arXiv · 2102.11768

Granular DeGroot Dynamics -- a Model for Robust Naive Learning in Social Networks

Gideon Amir·Itai Arieli·Galit Ashkenazi-Golan·Ron Peretz
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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{ $\frac{1}{m}$-DeGroot}. $\frac{1}{m}$-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, $\frac{1}{m}$-DeGroot dynamics is highly robust both to the presence of stubborn agents and to certain types of misspecifications.

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Gideon Amir, Itai Arieli, Galit Ashkenazi-Golan, Ron Peretz. 2021-02-23. Granular DeGroot Dynamics -- a Model for Robust Naive Learning in Social Networks. https://arxiv.org/abs/2102.11768

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