  We study the time series data of the racetrack betting market in the Japan
Racing Association (JRA). As the number of votes t increases, the win bet
fraction x(t) converges to the final win bet fraction x_{f}. We observe the
power law $(x(t)-x_{f})^{2} \propto t^{-\beta}$ with $\beta\simeq 0.488$. We
measure the degree of the completeness of the ordering of the horses using an
index AR, the horses are ranked according to the size of the win bet fraction.
AR(t) also obeys the power law and behaves as
$\mbox{AR}_{f}-\mbox{AR}(t)\propto t^{-\gamma}$ with $\gamma\simeq 0.589$,
where AR_{f} is the final value of AR. We introduce a simple voting model with
two types of voters-independent and herding. Independent voters provide
information about the winning probability of the horses and herding voters
decide their votes based on the popularities of the horses.This model can
explain two power laws of the betting process. The component ratio of the
independent voter to the herding voter is 1:3.
