As strong as the weakest node: The impact of misinformation in social networks

We study the impact of misinformation in a model of boundedly rational opinion formation in a social network. We capture misinformation via misspecified prior beliefs and consider networks that contain agents with differing social learning sophistication: identity social learners and quasi-Bayesian social learners. An attractive feature of the underlying heuristics is that in the baseline case absent misinformation both coincide with DeGroot updating, the arguably canonical boundedly rational heuristic. We find that the impact of misinformation depends upon the sophistication of the agents exposed to misinformation. If at least one misinformed agent engages in the simpler heuristic, identity social learning, then the long run opinions of all agents are extremely fragile to misinformation. Even if the perceived precision of the misinformation is infinitesimally small, the opinions of all agents in the network, identity and quasi-Bayesian social learners alike, converge to the misinformation state. Instead, if only the more sophisticated quasi-Bayesian social learners are exposed to misinformation, then the opinion process is robust to infinitessimal misinformation. Finally, we consider a general class of updating functions and show that there is a type of infinitessimal perturbation to the updating function of any agent such that the asymptotic consensus opinion is extremely fragile.