  We study the time change of the relation between the rank of a racehorse in
the Japan Racing Association and the result of victory or defeat. Horses are
ranked according to the win bet fractions. As the vote progresses, the
racehorses are mixed on the win bet fraction axis. We see the emergence of a
scale invariant relation between the cumulative distribution function of the
winning horse $x_{1}$ and that of the losing horse $x_{0}$. $x_{1}\propto
x_{0}^{\alpha}$ holds in the small win bet fraction region. We also see the
efficiency of the market as the vote proceeds. However, the convergence to the
efficient state is not monotonic. The time change of the distribution of a vote
is complicated. Votes resume concentration on popular horses, after the
distribution spreads to a certain extent. In order to explain scale invariance,
we introduce a simple voting model. In a `double' scaling limit, we show that
the exact scale invariance relation $x_{1}=x_{0}^{\alpha}$ holds over the
entire range $0\le x_{0},x_{1}\le 1$.
