The Niemeyer Formula Revisited

courtesy http://www.bundestag.de

We examine a formula that was mentioned earlier when the party-list system was tackled in the drafting of the 1987 Constitution and the Party-List Law.

In his dissenting opinion in the case Veterans Federation vs. Comelec (G.R. 136781, October 6, 2001), Justice Mendoza states that

“Rep. Tito R. Espinosa, co-sponsor of the bill which became R.A. No. 7941, explained that the system embodied in the law was largely patterned after the mixed party-list system in Germany. Indeed, the decision to use the German model is clear from the exchanges in the Constitutional Commission between Commissioners Blas F. Ople and Christian S. Monsod. The difference between our system and that of Germany is that whereas in Germany half (328) of the seats in the Bundestag are filled by direct vote and the other half (328) are filled through the party-list system, in our case the membership of the House of Representatives is composed of 80 percent district and 20 percent party-list representatives.

The party-list system of proportional representation is based on the Niemeyer formula, embodied in Art. 6(2) of the German Federal Electoral Law, which provides that, in determining the number of seats a party is entitled to have in the Bundestag, (the total number of) seats should be multiplied by the number of votes obtained by each party and then the product should be divided by the sum total of the second votes obtained by all the parties that have polled at least 5 percent of the votes. First, each party receives one seat for each whole number resulting from the calculation. The remaining seats are then allocated in the descending sequence of the decimal fractions.

The Niemeyer formula was adopted in R.A. No. 7941, §11. As Representative Espinosa said:

MR. ESPINOSA: This mathematical computation or formula was patterned after that of Niemeyer formula which is being practiced in Germany as formerly stated. As this is the formula or mathematical computation which they have seen most fit to be applied in a party-list system. This is not just a formula arrived at because of suggestions of individual Members of the Committee but rather a pattern which was already used, as I have said, in the assembly of Germany.”

Allocation of Seats in the 2005 Bundestag Election Using the Niemeyer Formula


courtesy of http://www.bundestag.de

In the 2005 Bundestag election, five parties, namely the Social Democratic Party (SPD), the Christian Democratic Union (CDU) and its Bavarian counterpart, the Christian Socialist Union (CSU), which forms a joint parliamentary group with the CDU but runs as a separate party, the Free Democratic Party (F.D.P), the Left Party and the Alliance 90/The Greens received at least five percent of all valid second votes cast, and were thus entitled to participate in the proportional allocation of seats at the federal level. The accumulated number of second votes of the 5 parties is 45,271,207. None of the other parties like the NPD and the Republicans that participated in the election reached the five percent threshold or received any constituency mandates; therefore, these were excluded from the apportionment process.



In the 2005 Bundestag Election, the number of seats mandated by the German Law is 598.

To determine the number of seats that qualified parties are entitled to, we compute the following:

1. The total number of available seats (598) should be multiplied by the number of votes obtained by each party and then the product should be divided by the sum total of the second votes obtained by all the parties that have polled at least 5 percent of the votes.

This is the ideal number of seats. See table below.



2. Each party receives one seat for each whole number resulting from the calculation.

This is the first round of seat allocation.


3. The remaining seats are then allocated in the descending sequence of the decimal fractions.

The total number of available seats is not filled up hence we have the second round of seat allocation to distribute the remaining number of seats which is 598 – 596 = 2.


Hence, the qualified parties are entitled to the number of seats given below:

This is the first stage of the Niemeyer Formula. The second stage of the Niemeyer Formula is to the allocation of the number of list seats per Land to each qualified party given the number of direct seats it obtained in the Land and the number of seats it is entitled to receive in that Land.

The Federal Republic of Germany is divided into 16 Lands. There are two votes in the Bundestag election, the first vote refers to a vote for a candidate of a party directly elected in the legislative district. The second vote refers to the party-list.

1. The number of direct seats from the legislative districts that a qualified party obtained in a given Land is subtracted from the number of seats that a qualified party is entitled to obtain in that Land.

     a. If the difference is positive, then it is the number of list seats that will be awarded to the     qualified to fill up the number of seats that the qualified is entitled to receive.

     b. If the difference is negative, no list seats will be awarded.

2. The sum of the number of direct seats and the number of list seats of a qualified party in a given Land is the actual number of seats that the qualified party receives in the Land.

If the number of direct seats is larger than the number of seats that a qualified party is entitled to receive, then there are overhang seats and the qualified party may actually receive more seats than the number of seats it is entitled to receive. The German Law allows this anomaly.

The Land level allocation of seats of each party is given below:

a) Christian Socialist Union (Table 6)

b) Social Democratic Party of Germany (Table 7)


 c) Free Democratic Party (Table 8)

 d) The Left Party (Table 9)


e) The Alliance 90/Greens Party (Table 10)



Hence, in the 2005 Bundestag election, 614 seats were allocated by the Niemeyer Method where the number of list seats is 315 and the number of direct seats is 299. See the Table 11.



Niemeyer Formula Clarified

  The Niemeyer Formula consists of two stages. In the first stage, the number of seats that each qualified party is entitled to receive is determine using the Largest Remainder Method. The second stage in the Formula is to determine the actual number of list seats that a qualified party shall receive per Land using the number of seats obtained in the first stage and the number of seats the qualified party won per Land.

 So the Formula that was referred to in the discussion of the Constitution, the deliberation of RA 7941 and the ruling of the Supreme Court is not really the Niemeyer Formula but the Largest Remainder Method.