Granular DeGroot dynamics – A model for robust naive learning in social networks

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. Golub and Jackson (2010) have shown that under DeGroot (1974) dynamics 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 “adversarial 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 $\frac{1}{m}$-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 adversarial agents and to certain types of misspecifications.