The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
The Wisdom of Crowds
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In the standard model of observational learning, n agents sequentially decide between two alternatives a or b, one of which is objectively superior. Their choice is based on a stochastic private signal and the decisions of others. Assuming a rational behavior, it is known that informational cascades arise, which cause an overwhelming fraction of the population to make the same choice, either correct or false. Assuming that each agent is able to observe the actions of all predecessors, it was shown by Bikhchandani, Hirshleifer, and Welch [1,2] that, independently of the population size, false informational cascades are quite likely. In a more realistic setting, agents observe just a subset of their predecessors, modeled by a random network of acquaintanceships. We show that the probability of false informational cascades depends on the edge probability p of the underlying network. As in the standard model, the emergence of false cascades is quite likely if p does not depend on n. In contrast to that, false cascades are very unlikely if p = p(n) is a sequence that decreases with n. Provided the decay of p is not too fast, correct cascades emerge almost surely, benefiting the entire population.