Seat allocation procedure after the election to the German Bundestag

The seat allocation procedure after the election to the German Bundestag or the seat allocation in the German Bundestag is the method of proportional representation in proportional representation , which is used to fill the German Bundestag after a Bundestag election . In the divisor method according to Sainte-Laguë , equality and immediacy of the choice are ensured.

Schematic distribution of seats in the Bundestag - symbolic image

Allocation of seats according to BWahlG

personalized proportional representation

After the seat allocation , which had been in effect since 1956, was declared unconstitutional by the Federal Constitutional Court on July 3, 2008 , because it could have negative voting weight , it was reformed on December 3, 2011 after a deadline set.

Among other things, a constitutional complaint was filed against this reform, which the Federal Constitutional Court approved and declared the amendment to the law null and void on July 25, 2012, as it could not, in principle, eliminate the main points of criticism and ensure the equality and immediacy of the election.

In October 2012, the Union, SPD, FDP and Greens agreed on a new regulation of the allocation of seats, which was passed by the Bundestag on February 21, 2013 and came into force on May 9, 2013.

The main changes are the balancing mandates , which maintain the proportion of votes after the occurrence of overhang mandates , and the elimination of negative voting weight through overhang mandates. However, compensatory mandates can have a similar effect, albeit much less often. However, this always occurs together with a compensating “positive” effect and is therefore not to be equated with the negative voting weight originally criticized by the Constitutional Court. Furthermore, compensation mandates can lead to a significant increase in the size of the Bundestag. Particularly in the case of overhang mandates from parties standing in only a few federal states, in the event of the elimination of the threshold clause or in the case of a growing number of parties represented in the Bundestag. Using the election polls shortly before the election to the 19th German Bundestag, it was simulated that the seat contingent could grow to 730 seats and 98.2% of all cases would exceed the size of the 18th German Bundestag . In fact, the 19th German Bundestag grew to 709 seats. The cause is primarily to be found in the overhang mandates of the CSU , which was able to win all direct mandates of Bavaria again in 2017, but performed significantly worse in the second vote distribution than in 2013. This led to overhang mandates from a nationwide relatively small party and, in turn, solves a correspondingly large party Demand for compensation mandates.

The allocation of seats is regulated in Section 6 of the Federal Election Act (BWahlG).

§ 6 Election according to state lists

(1) For the distribution of the seats to be filled according to Land lists, the second votes cast for each Land list are added together. If a constituency winner is non-party or belongs to a party that either failed because of the blocking or basic mandate clause or no state list has been approved for them, the second votes of the voters who voted for this constituency applicant with their first vote are not taken into account for the state lists. The number of such constituency winners is also deducted from the total number of members of the Bundestag.

(2) First, the Bundestag seats are assigned to the federal states according to their population figures (excluding foreigners) using the divisor method according to Sainte-Laguë, and these in turn, minus the above-mentioned direct mandates, are assigned to the state lists on the basis of the second votes to be taken into account. If the assignment is not clear, the Federal Returning Officer will decide .

(3) Only parties that have fulfilled the blocking or basic mandate clause (5% hurdle or three direct mandates) are taken into account when allocating the seats to the state lists. The exceptions are parties of national minorities.

(4) The number of seats on a country list determined in this way is reduced by the number of direct mandates won by the party in the country. The party retains direct mandates even if they exceed the number of seats it is entitled to. (Overhang mandates)

(5) The number of seats in the Bundestag will be increased and distributed to the state lists in accordance with paragraphs (1) - (4) until there are no overhang seats. (Compensation mandates)

(6) The seats of the thus enlarged Bundestag are now distributed to the parties to be considered and then to the state lists using the divisor method according to Sainte-Laguë. The direct mandates are deducted from the seats distributed on the country lists. The remaining seats will be filled from the state list in the order specified there. Constituency applicants who have won a direct mandate will not be included on the list. If there are more seats on a list than there are applicants, these will remain vacant.

(7) If, in the distribution of the seats according to paragraphs (2) - (6), a party to which more than half of the total number of second votes of all parties to be considered has not received more than half of the seats, it will receive further Seats are allocated until they occupy more than half of the seats. The seats of the party will be redistributed to the state lists according to (6) in the divisor procedure according to Sainte-Laguë, the direct mandates will be deducted and the remaining places according to the state list will be filled.

Allocation of seats using the example of the 2013 federal election

So far, three seat allocation procedures have been used in Bundestag elections . Until 1985, the distribution of seats was based on the D'Hondt procedure . This systematically favors larger parties and was replaced by the Hare-Niemeyer process . As a so-called "quota procedure with remaining balance to the largest fraction" it is the Sainte-Laguë method very similar, but takes account of its special rounding rule that awards the remaining seats in order of the largest decimal, paradoxes like the Alabama paradox or the apportionment paradox according to . In a study of January 4, 1999, the Federal Returning Officer came to the conclusion that the Sainte-Laguë procedure was preferable to the other two procedures. The 16th German Bundestag approved the replacement of the Hare-Niemeyer method to that effect on 24 January of 2008.

This seat allocation procedure in connection with the amendment to the federal electoral law that came into force on May 9, 2013 was applied for the first time in the elections to the 18th German Bundestag .

Preparation for election

The constituency of the Federal Republic for the 2013 Bundestag election

In order to maintain the equality of the elections, the constituency division of the federal territory must be checked and, if necessary, adjusted by a constituency commission consisting of the President of the Federal Statistical Office , a judge of the Federal Administrative Court and five other members before the elections . The aim is to keep the voting weight the same in each constituency. All German citizens within the meaning of Article 116 (1) of the Basic Law are taken into account . For the 2013 Bundestag elections, the population was as of December 31, 2010.

The allocation of constituencies is subject to the following principles in accordance with Section 3 (1) of the Federal Election Law :

National borders are to be observed
the currently 299 constituencies are distributed to the federal states according to the Sainte-Laguë procedure
the population of a constituency may not differ by more than 15% from the average constituency population.
the constituency should form a coherent area
the boundaries of the municipalities, districts and independent cities should be adhered to as far as possible

The constituency commission appointed by the Federal President must submit its report to the Federal Minister of the Interior within 15 months of the beginning of the electoral term .

Constituency allocation for the 2013 Bundestag election
state	Constituencies	+/-	changed constituencies
Schleswig-Holstein	11
Mecklenburg-Western Pomerania	06th	−1	12 - 13 - 14 - 15 - 16 - 17
Hamburg	06th		18 - 19 - 20
Lower Saxony	30th
Bremen	02
Brandenburg	10
Saxony-Anhalt	09
Berlin	12
North Rhine-Westphalia	64		115 - 116
Saxony	16
Hesse	22nd	+1	173 - 174 - 175 - 177 - 180
Thuringia	09
Rhineland-Palatinate	15th
Bavaria	45		215 - 216 - 217 - 222 - 224
Baden-Württemberg	38
Saarland	04th

Election result

← 2009Election to the 18th Bundestag 20132017 →

Final result - second votes
(71.5% turnout - 1.3% invalid votes)

%

50

40

30th

20th

10

0

41.5

25.7

8.6

8.4

4.8

4.7

2.2

1.3

1.0

1.8

Otherwise.

Gains and losses

compared to 2009

% p

8th

6th

4th

2

0

-2

-4

-6

-8th

-10

+7.7

+2.7

-3.3

-2.3

-9.8

+4.7

+0.2

-0.2

+1.0

-0.7

Otherwise.

The evaluation of the first votes did not produce a constituency winner who was not party to any party or belonged to a party that either failed due to the threshold clause or did not present a state list for the state. According to § 6 (1) BWahlG, all second votes of all parties to be considered are to be included in the further process.

Constituency seats (direct mandates)
Political party	Federation	SH	MV	HH	NI	HB	BB	ST	BE	NW	SN	HE	TH	RP	BY	BW	SL
CDU	191	9	6th	1	17th		9	9	5	37	16	17th	9	14th		38	4th
SPD	58	2		5	13	2	1		2	27		5		1
THE LEFT	4th								4th
GREEN	1								1
CSU	45														45
All in all	299	11	6th	6th	30th	2	10	9	12	64	16	22nd	9	15th	45	38	4th

Second votes
Political party		Federation	SH	MV	HH	NI	HB	BB	ST	BE	NW	SN	HE	TH	RP	BY	BW	SL
CDU	Number	14,921,877	638.756	369.048	285,927	1,825,592	96,459	482,601	485.781	508,643	3,776,563	994.601	1,232,994	477.283	958.655	-	2,576,606	212,368
CDU	%	34.1	39.2	42.5	32.1	41.1	29.3	34.8	41.2	28.5	39.8	42.6	39.2	38.8	43.3	-	45.7	37.8
SPD	Number	11,252,215	513.725	154,431	288.902	1,470,005	117.204	321.174	214.731	439.387	3,028,282	340.819	906.906	198.714	608.910	1,314,009	1,160,424	174,592
SPD	%	25.7	31.5	17.8	32.4	33.1	35.6	23.1	18.2	24.6	31.9	14.6	28.8	16.1	27.5	20.0	20.6	31.0
THE LEFT	Number	3,755,699	84,177	186,871	78.296	223.935	33.284	311,312	282,319	330.507	582,925	467.045	188,654	288,615	120,338	248.920	272,456	56,045
THE LEFT	%	8.6	5.2	21.5	8.8	5.0	10.1	22.4	23.9	18.5	6.1	20.0	6.0	23.4	5.4	3.8	4.8	10.0
GREEN	Number	3,694,057	153.137	37,716	112,826	391.901	40.014	64.182	46,585	220.737	760,642	113.916	313.135	60,511	169.372	552.818	623.294	31,998
GREEN	%	8.4	9.4	4.3	12.7	8.8	12.1	4.7	4.0	12.3	8.0	4.9	9.9	4.9	7.6	8.4	11.0	5.7
CSU	Number	3,243,569	-	-	-	-	-	-	-	-	-	-	-	-	-	3,243,569	-	-
CSU	%	7.4	-	-	-	-	-	-	-	-	-	-	-	-	-	49.3	-	-
Eligible voters		61,946,900	2,251,796	1,350,705	1,281,918	6,117,473	483,823	2,065,944	1,930,880	2,505,718	13,253,554	3,406,430	4,413,271	1,834,259	3,092,424	9,472,738	7,689,895	796.072
Voters		44,309,925	1,645,750	881.718	901.213	4,491,281	333.022	1,412,785	1,198,248	1,815,415	9,605,247	2,368,758	3,230,483	1,251,403	2,251,979	6,633,726	5,711,469	577,428
Voter turnout [%]		71.5	73.1	65.3	70.3	73.4	68.8	68.4	62.1	72.5	72.5	69.5	73.2	68.2	72.8	70.0	74.3	72.5
invalid second votes	Number	583.069	17,460	13,975	10,348	46,021	3,610	24,423	19,433	27,694	107.090	36,106	82,392	19,710	37,482	52,971	69,450	14,868
invalid second votes	%	1.3	1.1	1.6	1.2	1.0	1.1	1.7	1.6	1.5	1.1	1.5	2.6	1.6	1.7	0.8	1.2	2.6
valid second votes		43,726,856	1,628,290	867.743	890.829	4,445,260	329.412	1,388,362	1,178,815	1,787,815	9,498,157	2,332,652	3,148,091	1,231,693	2,214,497	6,580,755	5,642,019	562,560

“Voting is still carried out in the electoral system of personalized proportional representation, in which the election of persons in the constituency (first vote) is combined according to the principles of majority voting with the proportional representation of the parties' lists of countries (second vote). However, the determination of the final allocation of seats was amended. The conversion of the votes into Bundestag seats is now carried out in two distribution stages, each of which in turn includes two calculation steps. The legislative objective behind the new regulation is to maintain the basic character of proportional representation. As a result, each party should need roughly the same number of votes to get a seat.

All four calculation steps are carried out using the Sainte-Laguë / Schepers divisor method, which was already used for the 2009 Bundestag election. "

- Federal Returning Officer : "Election to the 18th German Bundestag on September 22, 2013 - Issue 3: Final results by constituency"

1st stage

In the first stage, paragraphs (1) - (4) of § 6 BWahlG are dealt with in two more extensive steps. Paragraphs (1) and (3) are already associated with the determination of the election results.

Step 1.1 - Seat contingents of the countries

For the overall distribution, the 598 Bundestag seats must first be divided into seat contingents for the individual states, based on the proportion of the population of the states in the federal territory. The aim is to count the same number of German citizens to be represented in each Bundestag seat and thus representatively for each MP. This requires a suitable divisor “population per Bundestag seat”, by which the various population figures of the states are divided in order to determine the seats to be allocated per state. In order to determine this, one uses the obvious one in a first step . ${\ displaystyle {\ text {Divisor}} D_ {0} = {\ frac {({\ text {Total population}})} {({\ text {Bundestag seats}})}} = {\ frac {74,324,165} {598}} = 124.287 {,} 901338}$

Allocation of seats to the federal states
start with an initial divisor				Correction of seat and determination of the final divisor
country	German population December 31, 2012	Initial divisor	seats rounded	Determination of the divisor range				Calculation of seats
country	German population December 31, 2012	Initial divisor	seats rounded	Number of seats plus 0.5	Candidate 1	Number of seats plus 1.5	Candidate 2	selected divisor	Seats
Schleswig-Holstein	2,686,085	: 124.287.901338 =	22nd	: 22.5 =	119,381, ...	: 23.5 =	114,301, ...	124,013.692308 < divisor ≤ 124,079.387978 selected divisor: 124,050	22nd
Mecklenburg-Western Pomerania	1,585,032		13	: 13.5 =	117,409, ...	: 14.5 =	109,312, ...		13
Hamburg	1,559,655		13	: 13.5 =	115,530, ...	: 14.5 =	107,562, ...		13
Lower Saxony	7,354,892		59	: 59.5 =	123,611, ...	: 60.5 =	121,568, ...		59
Bremen	575,805		5	: 5.5 =	104,691, ...	: 6.5 =	88,585, ...		5
Brandenburg	2,418,267		19th	: 19.5 =	124.013, ...	: 20.5 =	117,964, ...		19th
Saxony-Anhalt	2,247,673		18th	: 18.5 =	121,495, ...	: 19.5 =	115,265, ...		18th
Berlin	3,025,288		24	: 24.5 =	123,481, ...	: 25.5 =	118,638, ...		24
North Rhine-Westphalia	15,895,182		128	: 128.5 =	123,697, ...	: 129.5 =	122,742, ...		128
Saxony	4,005,278		32	: 32.5 =	123.239, ...	: 33.5 =	119,560, ...		32
Hesse	5,388,350		43	: 43.5 =	123,870, ...	: 44.5 =	121,086, ...		43
Thuringia	2,154,202		17th	: 17.5 =	123.097, ...	: 18.5 =	116,443, ...		17th
Rhineland-Palatinate	3,672,888		30th	: 30.5 =	120,422, ...	: 31.5 =	116,599, ...		30th
Bavaria	11,353,264		91	: 91.5 =	124.079, ...	: 92.5 =	122,737, ...		92
Baden-Württemberg	9,482,902		76	: 76.5 =	123,959, ...	: 77.5 =	122,360, ...		76
Saarland	919.402		7th	: 7.5 =	122,586, ...	: 8.5 =	108.164, ...		7th
All in all	74.324.165		597	${\ displaystyle {\ text {Divisorkandidat}} = {\ frac {({\ text {Population of countries}})} {({\ text {modified number of seats}})}}}$					598

When calculating with the initial divisor in the left half of the table, fewer seats are allocated to the countries than are available. This means that the divisor must be reduced. To do this, you divide the population of the federal states by a slightly increased number of assigned seats. The gradual increase of the previously determined seats by 0.5, 1.5 etc. is typical of the Sainte-Laguë method and mathematically takes into account the fairer commercial rounding . In addition, a large number of new divisor candidates are available to you due to the two increase levels applied to each federal state. In order not to catch a divisor that is too small now, one uses the half-open interval from the largest and second largest divisor candidates. Within this divisor range, the result is always the same mathematically, so that you can freely choose a divisor that is as round as possible from this range, with which you can start again with the allocation of seats.

Step 1.2 - Distribution of the seat contingents of the countries among the parties

In the next step, the seats of the states that have now been determined will be distributed to the state lists of the parties in the same principle, according to which paragraph (2) of § 6 BWahlG has been processed. For the initial divisor, the ratio of the second votes of all parties to be considered to the seat contingent of the corresponding country is used.

In the case of the State of Bavaria, the initial divisor already leads to a consistent distribution of seats. Nevertheless, one looks for the suitable divisor range in order to determine a divisor that is as round as possible. The initial divisor is slightly increased by a minimal decrease in the determined seats and a corresponding increase decreases it. The range from which the suitable divisor is selected is now formed from the smallest enlarged and the largest reduced.

exemplary: allocation of the seats of the state of Bavaria to the state lists
start with an initial divisor				Determination of the final divisor
Political party	Second votes	Initial divisor	seats rounded	Determination of the divisor range				Calculation of seats
Political party	Second votes	Initial divisor	seats rounded	Number of seats minus 0.5	Candidate 1	Number of seats plus 0.5	Candidate 2	selected divisor	Seats
CSU	3,243,569	: 58.253.434783 =	56	: 55.5 =	58,442, ...	: 56.5 =	57,408, ...	58,191,368421 <divisor ≤ 58,400,400000: 58,200	56
SPD	1,314,009		23	: 22.5 =	58,400, ...	: 23.5 =	55,915, ...		23
GREEN	552.818		9	: 8.5 =	65,037, ...	: 9.5 =	58,191, ...		9
THE LEFT	248.920		4th	: 3.5 =	71.120, ...	: 4.5 =	55,315, ...		4th
All in all	5,359,316		92	${\ displaystyle {\ text {Divisor candidate}} = {\ frac {({\ text {Second party votes}})} {({\ text {modified number of seats}})}}}$					92

In the state of Saxony, on the other hand, one seat too many is allocated in the first step. For this purpose, the seats are slightly reduced in line with the national contingents, for example, in order to increase the divisor. In order not to enlarge it too much, one uses the smallest and second smallest divisor to form the range. Here, too, a suitable divisor, which is as round as possible, is chosen with which the seats are redistributed. This is repeated until the specified total number of seats is reached.

exemplary: Allocation of the seats of the state of Saxony to the state lists
start with an initial divisor				Determination of the final divisor
Political party	Second votes	Initial divisor	seats rounded	Determination of the divisor range				Calculation of seats
Political party	Second votes	Initial divisor	seats rounded	Number of seats minus 0.5	Candidate 1	Number of seats minus 1.5	Candidate 2	selected divisor	Seats
CDU	994.601	: 59.886.90625 =	17th	: 16.5 =	60,278, ...	: 15.5 =	64,167, ...	60,278.848485 <divisor ≤ 61,967.090909: 61,000	16
THE LEFT	467.045		8th	: 7.5 =	62,272, ...	: 6.5 =	71,853, ...		8th
SPD	340.819		6th	: 5.5 =	61,967, ...	: 4.5 =	75,735, ...		6th
GREEN	113.916		2	: 1.5 =	75,944, ...	: 0.5 =	227,832, ...		2
All in all	1,916,381		33	${\ displaystyle {\ text {Divisor candidate}} = {\ frac {({\ text {Second party votes}})} {({\ text {modified number of seats}})}}}$					32

In this way, the seat contingents of each country are now distributed among the state party lists in order to determine how many MPs from which countries a party can send to the Bundestag based on its second votes.

Determination of the guaranteed minimum allocation of seats and completion of the first stage

After the Bundestag seats have been allocated to the states and these to the state lists of the parties, the electoral district winners of the states are now used. These so-called direct mandates have priority over all list candidates and fill the state party seats first. According to Paragraph (4) of Section 6 of the Federal Electoral Election Act, you will definitely move into the Bundestag, even if the allocated seating capacity is not sufficient for the parties. This excess of mandates is not uncommon in “smaller” countries, but it is also not excessive and increases the right to a seat of a party in the country and thus also in the Bundestag.

For the next stage, the minimum seating entitlements of all parties nationwide and thus the first enlargement of the Bundestag are determined.

Summary of the distribution of seats
country	Second votes				divisor	CDU / CSU				SPD				THE LEFT				GREEN				All in all
country	CDU / CSU	SPD	LEFT	GREEN	divisor	LS	DM	min	ÜM	LS	DM	min	ÜM	LS	DM	min	ÜM	LS	DM	min	ÜM	LS	DM	min	ÜM
SH	638.756	513.725	84,177	153.137	61,000	10	9	10	-	8th	2	8th	-	1	-	1	-	3	-	3	-	22nd	11	22nd	-
MV	369.048	154,431	186,871	37,716	60,000	6th	6th	6th	-	3	-	3	-	3	-	3	-	1	-	1	-	13	6th	13	-
HH	285,927	288.902	78.296	112,826	60,000	5	1	5	-	5	5	5	-	1	-	1	-	2	-	2	-	13	6th	13	-
NI	1,825,592	1,470,005	223.935	391.901	66,000	28	17th	28	-	22nd	13	22nd	-	3	-	3	-	6th	-	6th	-	59	30th	59	-
HB	96,459	117.204	33.284	40.014	65,000	1	-	1	-	2	2	2	-	1	-	1	-	1	-	1	-	5	2	5	-
BB	482,601	321.174	311,312	65,182	60,000	8th	9	9	1	5	1	5	-	5	-	5	-	1	-	1	-	19th	10	20th	1
ST	485.781	214.731	282,319	46,858	60,000	8th	9	9	1	4th	-	4th	-	5	-	5	-	1	-	1	-	18th	9	19th	1
BE	508,643	439.387	330.507	220.737	62,000	8th	5	8th	-	7th	2	7th	-	5	4th	5	-	4th	1	4th	-	24	12	24	-
NW	3,776,563	3,028,282	582,925	760,642	63,500	59	37	59	-	48	27	48	-	9	-	9	-	12	-	12	-	128	64	128	-
SN	994.601	340.819	467.045	113.916	61,000	16	16	16	-	6th	-	6th	-	8th	-	8th	-	2	-	2	-	32	16	32	-
HE	1,232,994	906.906	188,654	313.135	62,000	20th	17th	20th	-	15th	5	15th	-	3	-	3	-	5	-	5	-	43	22nd	43	-
TH	477.283	198.714	288,615	60,511	60,000	8th	9	9	1	3	-	3	-	5	-	5	-	1	-	1	-	17th	9	18th	1
RP	958.655	608.910	120,338	169.372	62,000	15th	14th	15th	-	10	1	10	-	2	-	2	-	3	-	3	-	30th	15th	30th	-
BY	3,243,569	1,314,009	248.920	552.818	58,200	56	45	56	-	23	-	23	-	4th	-	4th	-	9	-	9	-	92	45	92	-
BW	2,576,606	1,160,424	272,456	623.294	60,600	43	38	43	-	19th	-	19th	-	4th	-	4th	-	10	-	10	-	76	38	76	-
SL	212,368	174,592	56,045	31,998	65,000	3	4th	4th	1	3	-	3	-	1	-	1	-	-	-	-	-	7th	4th	8th	1
Σ	36,867,417					238 56	191 45	242 56	4 -	183	58	183	-	60	4th	60	-	61	1	61	-	598	299	602	4th
LS - state seats (attributable to the party); DM - Direct mandates obtained through the first votes; min - guaranteed minimum number of seats (LS + ÜM); ÜM - overhang mandates that occurred

Due to the four overhang mandates of the CDU in Brandenburg , Saxony-Anhalt , Thuringia and Saarland (1 each), the party's entitlement to a seat increases from 238 to 242 and the Bundestag thus grows from 598 to at least 602 members . There were no overhang mandates with the other parties to be considered, so that the CSU , SPD , Die Linke and Greens are entitled to 56, 183, 60 and 61 state seats, respectively, based on second votes.

2nd stage

At this point, the seat allocation process in previous elections was in principle complete. Overhang mandates ensure the voting character of the first vote, but violate the principle of proportional representation of the second vote. Since it has already happened that overhang seats in parliamentary groups occurred, the BVerfG found the following in its ruling on the constitutional complaint against the BWahlG reform of December 3, 2011:

"2.a) In the system created by the legislature of proportional representation associated with the election of persons, overhang mandates (Section 6 (5) BWG) are only acceptable to the extent that the basic character of the election as proportional representation is not eliminated.

b) The principles of equality of election and equality of opportunity for the parties are violated if there are overhang mandates of more than about half the size of a parliamentary group. "

- BVerfG : judgment of the Second Senate of July 25, 2012 - 2 BvF 3/11

This was taken into account in the new BWahlG regulation of May 9, 2013 through the introduction of compensation mandates. To this end, the Bundestag will be expanded in a first step so that overhang mandates are compensated and the second vote ratio is reflected in the distribution of seats. In a second, the seats are allocated to the state lists. Paragraphs (5) - (7) of § 6 BWahlG are implemented in the second stage. The basis of the distribution remains the Sainte-Laguë method.

Step 2.1 - Enlargement of the Bundestag due to the minimum seat entitlement

In the first step, the seats to which the parties are entitled based on the proportion of their second votes are determined at the federal level, taking into account their minimum seat claims from level 1.

The largest possible divisor that guarantees the minimum number of seats is determined for each party. To do this, you divide the number of their second votes by the number of their minimum seats reduced by 0.5. For each party you get a maximum divisor, of which you choose the smallest as the upper limit for the divisor range. All second votes are divided by this upper limit and the new number of seats is determined. The party from which this divisor originates receives its minimum seats by rounding up 0.5. For all other parties the new divisor is smaller than the one previously determined for them, which means that their number of seats tends to increase. The same divisor was used for all parties, so all seats have the same voting weight.

The second votes are now divided by the number of seats increased by 0.5 in order to obtain slightly reduced divisors. The largest of these then forms the lower limit of the divisor range, from which, as before, a divisor that is as round as possible is found, which is then used as a representative for the range.

Create compensation mandates
Determination of the upper divisor limit							Determination of the lower divisor limit
Political party	Second votes	Minimum seats minus 0.5	Parties divisor	Upper divisor limit	Seats NEW	Seats NEW plus 0.5	Divisor lower limit	selected divisor
CDU	14,921,877	: 241.5 =	61,788, ...	: 58,442.684684 =	255	: 255.5 =	58,402, ...	58,420
SPD	11,252,215	: 182.5 =	61,655, ...		193	: 193.5 =	58,150, ...
THE LEFT	3,755,699	: 59.5 =	63.120, ...		64	: 64.5 =	58,227, ...
GREEN	3,694,057	: 60.5 =	61.058, ...		63	: 63.5 =	58,174, ...
CSU	3,243,569	: 55.5 =	58,442, ...		56	: 56.5 =	57,408, ...
All in all	36,867,417				631

Step 2.2 - Allocation of seats to the state lists of the parties

The seat concessions determined in this way are distributed to the state lists so that each party is entitled to at least its direct mandates and thus the overhang mandates are dissolved.

This leads again via the Sainte-Laguë procedure, taking into account that the direct mandates represent the minimum for each country, for the distribution of seats among the countries. ${\ displaystyle {\ text {Initial divisor}} D_ {0} = {\ frac {({\ text {Second party votes}})} {({\ text {Bundestag seats}})}}}$

Since no party received more than half of the second votes of the parties to be considered, paragraph (7) of § 6 BWahlG does not apply.

The final allocation of seats is based on the following table:

Final distribution key
country	Second votes				divisor				CDU / CSU				SPD				THE LEFT				GREEN				All in all
country	CDU / CSU	SPD	LEFT	GREEN	CDU / CSU	SPD	LEFT	GREEN	LLP	DM	M.	AT THE	LLP	DM	M.	AT THE	LLP	DM	M.	AT THE	LLP	DM	M.	AT THE	LLP	DM	M.	AT THE
SH	638.756	513.725	84,177	153.137	59,500	58,500	60,000	60,500	2	9	11	1	7th	2	9	1	1	-	1	-	3	-	3	-	13	11	24	2
MV	369.048	154,431	186,871	37,716					-	6th	6th	-	3	-	3	-	3	-	3	-	1	-	1	-	7th	6th	13	-
HH	285,927	288.902	78.296	112,826					4th	1	5	-	-	5	5	-	1	-	1	-	2	-	2	-	7th	6th	13	-
NI	1,825,592	1,470,005	223.935	391.901					14th	17th	31	3	12	13	25th	3	4th	-	4th	1	6th	-	6th	-	36	30th	66	7th
HB	96,459	117.204	33.284	40.014					2	-	2	1	-	2	2	-	1	-	1	-	1	-	1	-	4th	2	6th	1
BB	482,601	321.174	311,312	65,182					-	9	9	-	4th	1	5	-	5	-	5	-	1	-	1	-	10	10	20th	-
ST	485.781	214.731	282,319	46,858					-	9	9	-	4th	-	4th	-	5	-	5	-	1	-	1	-	10	9	19th	-
BE	508,643	439.387	330.507	220.737					4th	5	9	1	6th	2	8th	1	2	4th	6th	1	3	1	4th	-	15th	12	27	3
NW	3,776,563	3,028,282	582,925	760,642					26th	37	63	4th	25th	27	52	4th	10	-	10	1	13	-	13	1	74	64	138	10
SN	994.601	340.819	467.045	113.916					1	16	17th	1	6th	-	6th	-	8th	-	8th	-	2	-	2	-	17th	16	33	1
HE	1,232,994	906.906	188,654	313.135					4th	17th	21st	1	11	5	16	1	3	-	3	-	5	-	5	-	23	22nd	45	2
TH	477.283	198.714	288,615	60,511					-	9	9	-	3	-	3	-	5	-	5	-	1	-	1	-	9	9	18th	-
RP	958.655	608.910	120,338	169.372					2	14th	16	1	9	1	10	-	2	-	2	-	3	-	3	-	16	15th	31	1
BY	3,243,569	1,314,009	248.920	552.818	-				11	45	56	-	22nd	-	22nd	−1	4th	-	4th	-	9	-	9	-	46	45	91	-1
BW	2,576,606	1,160,424	272,456	623.294	59,500				5	38	43	-	20th	-	20th	1	5	-	5	1	10	-	10	-	40	38	78	2
SL	212,368	174,592	56,045	31,998	59,500				-	4th	4th	-	3	-	3	-	1	-	1	-	1	-	1	1	5	4th	9	1
Σ	14,921,877 3,243,569	11,252,215	3,755,699	3,694,057					64 11	191 45	255 56	13 -	135	58	193	10	60	4th	64	4th	62	1	63	2	332	299	631	29
Σ	36,867,417
LLP - state list places (M-DM); DM - Direct mandates obtained through the first votes; M - Bundestag mandates ; AM - compensation mandates

The SPD has lost a list position in Bavaria due to the compensation mandates. This phenomenon, which is similar to the negative voting weight, can occur, but cannot be compared with the actual one, as the SPD also won eleven additional seats.

Before 1956

In Article 38 of the Basic Law for the Federal Republic of Germany , in addition to the basic features of the election, the election of the members of the German Bundestag should be specified in more detail in a federal law. Since the parliamentary council could not agree on a constitutional definition of the electoral system, a separate electoral law was passed for the election to the first German Bundestag .

1949

The electoral law created especially for the first federal election came into force on June 15, 1949 in cooperation with the Parliamentary Council and the military governors .

The number of seats in the Bundestag was set at at least 400 in Section 8, as was the distribution of the seat contingents among the federal states. The federal states should also cover 60% of their contingents through constituency mandates, i.e. divide their federal state into a corresponding number of constituencies.

Bundestag seats in 1949
country	Seats	of which constituencies (60%)	of which list positions (40%)
to bathe	11 (+1)	7th	4 (+1)
Bavaria including Lindau	78	47	29
Bremen	4 (+1)	3	1 (+1)
Hamburg	13	8th	5
Hesse	36	22nd	14th
Lower Saxony	58	34	24
North Rhine-Westphalia	109	66	43
Rhineland-Palatinate	25th	15th	10
Schleswig-Holstein	23	14th	9
Württemberg-Baden	33	20th	13
Württemberg-Hohenzollern	10	6th	4th
All in all	400 (+2)	242	158 (+2)

Each voter had one vote, which also determined the electoral district winner, as well as the distribution of votes of the parties in the country and thus their shares in the country seats. The Bundestag election was thus broken down at state level - a threshold clause of five percent and a basic mandate clause from a direct mandate were taken into account in every federal state, not just nationwide.

The state seat contingents were allocated to the parties according to the D'Hondt procedure on the basis of the state votes. After the direct mandates were withdrawn, the remaining seats were filled according to the state lists.

When overhang mandates occurred, it was originally intended to add them to the state seat contingent and to redistribute the seats. However, this procedure would not rule out the possibility of others occurring, nor would it be clarified how to deal with these. When the regional returning officers announced on this problem that they would simply ignore this regulation if it should emerge, the military government passed a change in the law on August 5, 1949, nine days before the election, after which overhang mandates would simply be left as such. They also introduced that the state seat contingents are reduced by the number of non-party constituency winners before the allocation.

One overhang mandate each occurred with the SPD in Bremen and the CDU in Baden.

If a direct mandate became vacant (through resignation, resignation, dismissal or death), by-elections were held. There were 14 of them in the first parliamentary term. In the case of a list mandate, on the other hand, a replacement occupied the vacant space.

Occupied Berlin was allowed to send eight MPs in an advisory capacity to the Bundestag until it came into the scope of the Basic Law.

Web links

www.bundeswahlleiter.de - The official website of the Federal Returning Officer with graphics and reports on all federal elections

www.gesetze-im-internet.de - The Federal Election Act

www.youtube.com - "Bundestag election - from the votes to the distribution of seats", user: DorFuchs

Documents

BTW13 BWG constituency division.pdf - "Consolidated version of the constituency division for the election to the 18th German Bundestag"
BTW13 Heft3.pdf - "Election to the 18th German Bundestag on September 22nd, 2013 - Booklet 3: Final results according to constituencies"

Individual evidence

↑ BVerfGE, 2 BvC 1/07 of July 3, 2008. In: Bundesverfassungsgericht. July 3, 2008, accessed September 20, 2017 .

↑ Nineteenth Act to Amend the Federal Electoral Act

↑ mehr-demokratie.de ( Memento of the original from March 8, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2
↑ ^a ^b Judgment on the constitutional complaint against the 19th BWahlGÄndG, 2 BvF 3/11 of July 25, 2012. In: Bundesverfassungsgericht. July 25, 2012. Retrieved September 20, 2017 .
↑ Twenty-second law amending the federal electoral law
↑ Interior Committee of the Bundestag, Committee printed matter 17 (4) 624 C ( Memento from October 5, 2013 in the Internet Archive ) (PDF; 314 kB)
↑ Lack of space in the plenary hall. In: faz.net. September 19, 2017. Retrieved September 20, 2017 .
↑ Simulation of the results of the Bundestag election on September 24, 2017 with regard to the size of the Bundestag. (PDF; 222 kB) In: www.zu.de. September 13, 2017. Retrieved September 20, 2017 .
↑ The new Bundestag is the largest and most expensive of all time. In: welt.de. September 25, 2017. Retrieved September 25, 2017 .
↑ The divisor method with rounding off. In: Wahlrecht.de. April 15, 2012. Retrieved September 21, 2017 .
↑ The quota procedure with the remaining balance according to the largest fractions. In: Wahlrecht.de. September 1, 2013, accessed September 21, 2017 .
↑ The divisor method with standard rounding. In: Wahlrecht.de. April 17, 2013. Retrieved September 21, 2017 .
↑ ^a ^b constituency division. In: bundeswahlleiter.de. April 17, 2013. Retrieved September 21, 2017 .
↑ Federal Returning Officer: Federal result - final result of the federal election 2013 ( Memento of 16 May 2016 in the Internet Archive )
↑ BTW13 Heft3.pdf - Table 3, p. 252.
↑ BTW13 Heft3.pdf - Table 1.2, p. 14ff.
↑ BTW13 Heft3.pdf - Section 8 “Calculation procedure and distribution of seats in accordance with Section 6 of the Federal Election Act (BWG) for the 2013 Bundestag election” Introduction (8.1), p. 312.
↑ BTW13 Heft3.pdf - Table 8.2.1, p. 325.
↑ BTW13 Heft3.pdf - Table 8.2.2, p. 332.
↑ BTW13 Heft3.pdf - Table 8.2.2, p. 330.
↑ BTW13 Heft3.pdf - Tables 8.1.2 - 8.1.3, pp. 314–319.
↑ BTW13 Heft3.pdf - Table 8.2.3, p. 334.
↑ BTW13 Heft3.pdf - Tables 8.1.5 - 8.1.6, pp. 314ff, 321 - 324
↑ ^a ^b ^c History of the right to vote in the Bundestag. In: Wahlrecht.de. May 8, 2013, accessed November 4, 2017 .
^ Election law for the first Bundestag and the first Federal Assembly of the Federal Republic of Germany. In: Archive. March 3, 2004, accessed November 4, 2017 .
↑ ^a ^b Federal Parliament election 1949 - votes and seats in the federal states. In: www.election.de. Retrieved November 4, 2017 .
↑ Law of August 5, 1949 to supplement and amend the electoral law for the first Bundestag and the first Federal Assembly of the Federal Republic of Germany of June 15, 1949. In: Archive. March 3, 2004, accessed November 4, 2017 .

[1] BVerfGE, 2 BvC 1/07 of July 3, 2008. In: Bundesverfassungsgericht. July 3, 2008, accessed September 20, 2017 .

[2] Nineteenth Act to Amend the Federal Electoral Act