  We propose a method of detecting a phase transition in a generalized P\'olya
urn in an information cascade experiment. The method is based on the asymptotic
behavior of the correlation $C(t)$ between the first subject's choice and the
$t+1$-th subject's choice, the limit value of which, $c\equiv \lim_{t\to
\infty}C(t)$, is the order parameter of the phase transition. To verify the
method, we perform a voting experiment using two-choice questions. An urn X is
chosen at random from two urns A and B, which contain red and blue balls in
different configurations. Subjects sequentially guess whether X is A or B 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
set $q\in \{5/9,6/9,7/9,8/9\}$ by controlling the configurations of red and
blue balls in A and B. The (average) lengths of the sequence of the subjects
are 63, 63, 54.0, and 60.5 for $q\in \{5/9,6/9,7/9,8/9\}$, respectively. We
describe the sequential voting process by a nonlinear P\'olya urn model. The
model suggests the possibility of a phase transition when $q$ changes. We show
that $c>0\,\,\,(=0)$ for $q=5/9,6/9\,\,\,(7/9,8/9 )$ and detect the phase
transition using the proposed method.
