Phase transition to two-peaks phase in an information cascade voting experiment

Observational learning is an important information aggregation mechanism. However, it occasionally leads to a state in which an entire population chooses a sub-optimal option. When it occurs and whether it is a phase transition remain unanswered. To address these questions, we performed a voting experiment in which subjects answered a two-choice quiz sequentially with and without information about the prior subjects' choices. The subjects who could copy others are called herders. We obtained a microscopic rule regarding how herders copy others. Varying the ratio of herders led to qualitative changes in the macroscopic behavior in the experiment of about 50 subjects. If the ratio is small, the sequence of choices rapidly converges to the true one. As the ratio approaches 100%, convergence becomes extremely slow and information aggregation almost terminates. A simulation study of a stochastic model for 10^{6} subjects based on the herder's microscopic rule showed a phase transition to the two-peaks phase, where the convergence completely terminates, as the ratio exceeds some critical value.