There was this talk (by M. Dahleh) on modeling whether distributed learning occurs in a social network, i.e., is the crowd always right? The problem model was like this: there is a “truth” which is either 0 or 1, representing some binary preference. Then in a connected graph representing a learning network, each node makes a binary decision (0 or 1 again) based on an independent noisy read on the “truth,” as well as the decisions made by some or all of its neighbors who have already made a decision. (Each nodal decision is made once and binding, so there is a predefined decision-making order among the nodes.)

This is an interesting question because at first thought, one would think that in a large enough network, a sufficient number of independent reads on the truth will occur in the aggregate to allow at least the later-deciding nodes to get a really good estimate of the truth. This is the basis of the folk belief in “wisdom of the crowd.” However, this is not what happens all the time.

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