  We study the process of information dispersal in a network with communication
errors and local error-correction. Specifically we consider a simple model
where a single bit of information initially known to a single source is
dispersed through the network, and communication errors lead to differences in
the agents' opinions on this information.
  Naturally, such errors can very quickly make the communication completely
unreliable, and in this work we study to what extent this unreliability can be
mitigated by local error-correction, where nodes periodically correct their
opinion based on the opinion of (some subset of) their neighbors. We analyze
how the error spreads in the "early stages" of information dispersal by
monitoring the average opinion, i.e., the fraction of agents that have the
correct information among all nodes that hold an opinion at a given time. Our
main results show that even with significant effort in error-correction, tiny
amounts of noise can lead the average opinion to be nearly uncorrelated with
the truth in early stages. We also propose some local methods to help agents
gauge when the information they have has stabilized.
