Learning Through the Grapevine: The Impact of Message Mutation, Transmission Failure, and Deliberate Bias

Abstract

We study how communication platforms, or a society more generally, can improve social learning without censoring or fact-checking messages. We analyze learning as a function of social network depth (how many times information is relayed) and breadth (the number of relay chains accessed). Noise builds up as depth increases, so learning requires greater breadth. We characterize sharp thresholds for breadths above which receivers learn fully and below which they learn nothing. However, slight uncertainty about the noise structure can destroy learning even in arbitrarily broad networks. Learning can be restored by capping depth or, if that is not possible, limiting breadth (e.g., by capping the number of people to whom someone can forward a given message). Although it reduces total communication, limiting breadth increases the fraction of received messages originating closer to the receiver, thereby increasing the signal to noise ratio. We also extend our model to study learning from message survival when people are more likely to pass messages with one conclusion than another. We find that as depth grows, all information comes from either the total number of messages received or their content, but the learner does not need to pay attention to both. Thus, a forwarding cap for the policymaker is robust to whether receivers are fully Bayesian or naive and simply count relative rates of messages they receive.