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]