The mathematical theorem behind information cascades is

*Bayes' Law*(or Bayes' Rule). It says that given two events*A*and*B*, if you know that*A*occurred, you may change your assessment of the likelihood of*B*, compared to when you are uncertain whether*A*has occurred or not:P[B|A] ≠ P[B]

Furthermore, the probabilities of the two events are related by

*Bayes' Rule*:P[B|A] = P[A|B] (P[B] / P[A])

This is because:

P[B|A] P[A] = P[A∩B] = P[A|B] P[B]