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

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 1/ -DeGroot. 1/ -DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, 1/ -DeGroot dynamics is highly robust both to the presence of adversarial agents and to certain types of misspecifications.