and so on up to many pre-election processes, while the average votes gained by candidate
in n-th subprocess is
fn(c)=c1c2...cn (4)
The total votes gained by candidates are then can be assumed as the multiplicative
process since the total votes gained by candidate eventually in the election after large
amount of n is
v= fn(c)=c1c2...cn
(5)
While v denotes the total votes for candidates in the ballot, and N(v) as the number of
candidates that received the fraction votes v, we can have the histogram of N(v) vs v as
the statistical distribution of the whole voting process. This explanation was also
proposed by Filho, et. al. (2002) on finding the power-law characteristic in Brazilian
election.
It is very interesting that the histogram resulted (N(v) vs v) is not a gaussian one but a
power-law characters showing that the election result is somehow a self-organized and
critical social conditions. For the election of the member of Regional Representative
Council (DPD: Dewan Perwakilan Daerah) that elected for the first time in 2004, the
distribution of the number of candidates N receiving fraction of votes v followed a
power-law N(v) ~ vα with fitted α≈ 1 . This fact can be seen in figure 1.
The double-log histogram of the result of DPD (Regional Representative Council) 2004 election.
In the other hand, the result of election for House of Representatives is also power-law
but with approximated exponent lower than 1. The signature of the power-law
distribution is not only seen in the result of 2004 election but also in the previous (1999)