How the Saint-Lague Method Actually Works

Members of the Parliament and the government have decided to pass the Elections Law Bill into an applicable law on July 21^st 2017. One of the provision contained in the Law is the implementation of Saint-Lague method as a method for conversing votes into parliamentary seat allocation (previously, election management body in Indonesia had been using the Hare Quota method).

Friday (07/21) in the early morning, the Chairman of the Parliament, Setya Novanto, knocked the hammer on his table as a sign of consensus among the Parliament members to pass the Elections Law Bill into an applicable law. One of the consequence from the passing of the law is that for now on, election management body in Indonesia shall use Saint-Lague method to converse votes into parliamentary seat allocation.

“(With Saint-Lague) we divide the total votes acquired by political party with divisor index of 1, and then divide it sequentially with divisor index of 3, 5, 7, and so on,” as quoted from the Article 420 of the Elections Law Bill.

In a proportional election system (where there are more than one available seats in every electoral area), there are two ways of conversing votes into seats: quota method and divisor method.

Quota Method

Quota is the minimum “price” that needs to be paid by political party in order to get one parliamentary seat. In Indonesia, the quota is called BPP (bilangan pembagi pemilih or voters divisor index). There are several method to determine a quota, but the most common are the Hare Quota and Droop Quota method.

The Hare Quota index is determined by dividing the number of total votes with the total parliamentary seats available (Hare Quota = Total votes / Total parliamentary seats). Meanwhile, the Droop Quota index is determined by dividing the total number of votes with the number of total parliamentary seats available plus one (Droop Quota = total votes / total parliamentary seats + 1).

Then, the total parliamentary seats acquired by each political party is determined by dividing the total votes acquired by the party with the quota index. This division will result in a non-integer number with few decimal places. The seats will then be allocated by the integer numbers, and then the last remaining seats are allocated based on the highest decimal remainder.

This Hare Quota method has been implemented in Indonesia since 1948, based on Law No.27/1948, until 2012. The upcoming 2019 National Elections, based on the new Elections Law, will be the first election in Indonesia that uses the Saint-Lague method.

Saint-Lague

The Saint-Lague method is a part of a big branch of method called divisor method. With the divisor method, the total votes acquired by a political party will be divided by a fixed divisor index. The divisor index in the divisor method are 1, 3, 5, and so on. These indexes were determined by France mathematician, Andre Saint-Lague, in 1910. Meanwhile, another branch of the divisor method called D’Hondt method uses integer number as its divisor (1, 2, 3, 4, and so on).

“There are four steps that need to be considered in implementing the Saint-Lague method,” says Heroik Pratama, a researcher from the Association for Elections and Democracy (Perludem).

Firstly, we need to sum up the total votes acquired by every candidate from a party so we can know the total votes acquired by the party. Secondly, we then need to divide the total votes of the party with divisor index of 1, 3, 5, 7, and so on. Thirdly, we need to sort the result of the division from the highest to the lowest. Fourthly, the sorted result is then used as the basis for seats allocation.

As an illustration, assume that there are 10 seats available that need to be allocated to four political parties that acquired votes as follows, respectively: 25,000, 19,000, 12,000, and 8,000. The allocation method is represented in the table below.

	1	3	5	7
Party A	25,000 [1]	8,333 [4]	5,000 [7]	3,571 [10]
Party B	19,000 [2]	6,333 [6]	3,800 [9]	2,714
Party C	12.000 [3]	4,000 [8]	2,400	1,714
Party D	8,000 [5]	2,667	1,600	1,143

* The number inside this [] bracket represents the ranking of the result from the division of total votes and the divisor index

From the table we can conclude that Party A gets four seats, Party B gets three seats, Party C gets two seats, and Party D only gets one seat.

The result from using Saint-Lague method is quite similar with the result from Hare Quota, compared to other methods such as D’Hondt or Modified Saint-Lague. If we implemented the Saint-Lague method for the result of 2014 Elections, we will get a not-so-much different result than the actual.

No.	Party Name	Hare Quota (seats)	Saint-Lague (seats)	Difference
1	Nasdem	36	33	-3
2	PKB	47	48	1
3	PKS	40	39	-1
4	PDI-P	109	110	1
5	Golkar	91	94	3
6	Gerindra	73	73	0
7	Demokrat	61	61	0
8	PAN	48	47	-1
9	PPP	39	39	0
10	Hanura	16	16	0
	Total	560	560

August Mellaz, the Executive Director of Syndication for Elections and Democracy (SPD), says, Saint-Lague method provide a better guarantee in treating every political party more neutral and fairer in seats allocation process. With Saint-Lague method, party with more votes will get more seats, while party with less votes will get less seats. In other words, Saint-Lague method is more proportionate.