Learning through the grapevine and the impact of the breadth and depth of social networks.

We study how communication platforms can improve social learning without censoring or fact-checking messages, when they have members who deliberately and/or inadvertently distort information. Message fidelity depends on social network depth (how many times information can be relayed) and breadth (the number of others with whom a typical user shares information). We characterize how the expected number of true minus false messages depends on breadth and depth of the network and the noise structure.