Phase transition to a two-peak 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 suboptimal option. When this occurs and whether it is a phase transition remain unanswered. To address these questions we perform a voting experiment in which subjects answer a two-choice quiz sequentially with and without information about the prior subjects' choices. The subjects who could copy others are called herders. We obtain a microscopic rule regarding how herders copy others. Varying the ratio of herders leads to qualitative changes in the macroscopic behavior of about 50 subjects in the experiment. If the ratio is small, the sequence of choices rapidly converges to the correct 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 shows a phase transition to the two-peak phase, where the convergence completely terminates as the ratio exceeds some critical value.