Rational Disagreement and the Fragility of Social Learning : Identification Failures with Noisy Communication

We examine how agents learn when information from original sources only reaches them after noisy relay. In the presence of random mutation of message content and transmission failures, there is a sharp threshold such that a receiver fully learns if and only if they have access to more chains than the threshold number and they perfectly understand the noise process. However, even slight uncertainty over the relative rates of mutations makes learning from long chains impossible, no matter how many distinct sources information emerges from. The identification failure is that an agent cannot distinguish uncertainty about the state from uncertainty about the noise in communication. This result rationalizes long-run disagreement: even agents with a common prior and access to an arbitrary number of primary sources can end up with different beliefs if their network positions place them at different distances relative to primary sources