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 that under the DeGroot dynamics agents reach a consensus which 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 `bot' that does not adhere to the updating rule, can sway the public consensus to any other value. We introduce a variant of the DeGroot dynamics which we call \emph{ $\varepsilon$-DeGroot}. The $\varepsilon$-DeGroot dynamics approximates the standard DeGroot dynamics and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to the standard DeGroot dynamics, the $\varepsilon$-DeGroot dynamics is highly robust both to the presence of bots and to certain types of misspecifications.

中文翻译：

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社交网络中的健壮天真学习

我们研究了社交网络中的意见交换模型，在该模型中实现了世界状态，并且每个代理都收到实现状态的零均值噪声信号。从Golub和Jackson得知，在DeGroot动力学下，代理商达成了一个共识，当网络很大时，这个共识已接近世界的现状。但是，DeGroot的动态性非常不强壮，并且存在一个不遵守更新规则的“机器人”，可以将公众的共识转移到其他任何价值上。我们介绍了DeGroot动力学的一种变体，我们称之为\ emph {$ \ varepsilon $ -DeGroot}。$ \ varepsilon $ -DeGroot动力学近似于标准的DeGroot动力学，就像DeGroot动力学一样，它是马尔可夫定律。我们证明，与标准的DeGroot动态相比，