# Information Cascade and Bayes Formula

## Abstract

We consider a voting experiment using two-choice questions. An urn X is chosen at random from two urns A or B, which contain red and blue balls in different configurations. Subjects sequentially guess whether X is A or B by using information about the prior subjects’ choices and the color of a ball randomly drawn from X. The color tells the subject which is X with probability *q*. We describe the sequential voting process by a stochastic differential equation. The model suggests the possibility of a phase transition when *q* changes. When there is not the phase transition, in the limit *t* →*∞*, we can choose the correct pod. When there is the phase transition, the votes sometimes converge to the wrong equilibrium. We consider the method to estimate the ratio of red and blue balls, *q* using the Bayes formula, and study whether we correct the wrong decisions even if there is the phase transition.

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