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

TL;DR

This paper introduces a new variant of DeGroot opinion dynamics, called rac{1}{m}-DeGroot, which maintains consensus close to the true state while being highly robust to stubborn agents and misspecifications in social networks.

Contribution

The paper proposes rac{1}{m}-DeGroot dynamics, a robust alternative to standard DeGroot, improving resilience to stubborn agents and model misspecifications.

Findings

rac{1}{m}-DeGroot approximates DeGroot dynamics with increased robustness.

The new model is resilient to stubborn agents influencing consensus.

It remains stationary and Markovian like the original DeGroot model.

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.