  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.
