• Title: Bundestagswahl 2025 - Neues Wahlverfahren kurz erklärt

  • Series: Bundestagswahl 2025

  • YouTube-Title: Bundestagswahl 2025 - Neues Wahlverfahren kurz erklärt

  • Bright video: Watch on YouTube

  • Dark video: Watch on YouTube

  • Ad-free video: Watch Vimeo video

  • Forum: Ask a question in Mattermost

  • PDF: Download PDF version of the bright video

  • Dark-PDF: Download PDF version of the dark video

  • Print-PDF: Download printable PDF version

  • Python file: Download Python file

  • Thumbnail (bright): Download PNG

  • Thumbnail (dark): Download PNG

  • Subtitle on GitHub: btw_de01_sub_eng.srt

  • Download bright video: Link on Vimeo

  • Download dark video: Link on Vimeo

  • Other languages: English version

  • Timestamps (n/a)
  • Subtitle in English

    1 00:00:00,520 –> 00:00:04,720 Hello and welcome to this

    2 00:00:02,679 –> 00:00:06,480 video about the election system for

    3 00:00:04,720 –> 00:00:09,080 the “Bundestagswahl 2025”.

    4 00:00:06,480 –> 00:00:10,559 Mainly, I want to explain

    5 00:00:09,080 –> 00:00:12,599 how the German parliament (Bundestag)

    6 00:00:10,559 –> 00:00:14,400 is put together after each voter

    7 00:00:12,599 –> 00:00:16,800 has given his two votes (There are Erststimme and Zweitstimme)

    8 00:00:14,400 –> 00:00:18,480 Often one says that the whole

    9 00:00:16,800 –> 00:00:20,000 election system is really

    10 00:00:18,480 –> 00:00:22,039 complicated since it is adapted again and again.

    11 00:00:20,000 –> 00:00:24,080 However, in this video

    12 00:00:22,039 –> 00:00:26,080 you will see that the entire

    13 00:00:24,080 –> 00:00:28,599 distribution procedure is actually

    14 00:00:26,080 –> 00:00:30,400 quite simple and the first thing to

    15 00:00:28,599 –> 00:00:32,920 remember is that the whole

    16 00:00:30,400 –> 00:00:35,559 election prodecure essentially has three

    17 00:00:32,920 –> 00:00:37,600 layers. On the outermost layer,

    18 00:00:35,559 –> 00:00:40,320 we have the entire federal republic of

    19 00:00:37,600 –> 00:00:42,640 Germany. This defines the electoral area.

    20 00:00:40,320 –> 00:00:45,360 But it is split, on the one hand,

    21 00:00:42,640 –> 00:00:49,640 into 16 states. And the other hand

    22 00:00:45,360 –> 00:00:51,480 it is split into 299 electoral districts (Wahlkreise)

    23 00:00:49,640 –> 00:00:53,559 There, it is important to know that a Wahlkreis

    24 00:00:51,480 –> 00:00:55,800 always lies completely inside a

    25 00:00:53,559 –> 00:00:57,079 given state. Then these districts are

    26 00:00:55,800 –> 00:00:59,399 enumerated from 1-299.

    27 00:00:57,079 –> 00:01:03,040 For example for the state Hessia

    28 00:00:59,399 –> 00:01:05,799 we find the numbers 166 to

    29 00:01:03,040 –> 00:01:08,479 187. And it’s important to know that

    30 00:01:05,799 –> 00:01:11,080 in each district, the given ballot paper

    31 00:01:08,479 –> 00:01:14,680 looks different. In that sense, voting

    32 00:01:11,080 –> 00:01:16,720 happens on the layer of the electoral districts.

    33 00:01:14,680 –> 00:01:18,200 If we pick out one of them,

    34 00:01:16,720 –> 00:01:21,000 then we see that within the

    35 00:01:18,200 –> 00:01:23,560 given Wahlkreis, so-called constituency candidates (Wahlkreisbewerber)

    36 00:01:21,000 –> 00:01:25,720 compete against each other.

    37 00:01:23,560 –> 00:01:28,960 They are also called “direct candidates” because

    38 00:01:25,720 –> 00:01:30,759 one can vote for them directly, as a vote for a person.

    39 00:01:28,960 –> 00:01:33,600 That is exactly what you can do with your first vote.

    40 00:01:30,759 –> 00:01:35,600 This is one is called “Erststimme”.

    41 00:01:33,600 –> 00:01:38,479 Your own Erstimme, which you can use,

    42 00:01:35,600 –> 00:01:41,200 is only applicable in the given

    43 00:01:38,479 –> 00:01:43,439 electoral district. On the other hand, your second vote,

    44 00:01:41,200 –> 00:01:46,079 the so-called “Zweitstimme” is stronger.

    45 00:01:43,439 –> 00:01:48,079 It’s applicable to the whole state you are living in.

    46 00:01:46,079 –> 00:01:50,200 However, with this Zweitstimme you do not vote for a single person anymore

    47 00:01:48,079 –> 00:01:52,880 but for a whole list of people

    48 00:01:50,200 –> 00:01:54,520 that is given by a political party.

    49 00:01:52,880 –> 00:01:57,200 This means each party in a given state

    50 00:01:54,520 –> 00:01:59,960 can state a whole list of candidates

    51 00:01:57,200 –> 00:02:01,960 and the voter can use his Zweitstimme

    52 00:01:59,960 –> 00:02:04,159 to say which party he wants.

    53 00:02:01,960 –> 00:02:07,039 In the following sense,

    54 00:02:04,159 –> 00:02:09,599 the Zweitstimme is stronger than the Erststimme

    55 00:02:07,039 –> 00:02:11,360 because the total number of votes in the Zweitstimme

    56 00:02:09,599 –> 00:02:13,920 determine the proportions of the parties

    57 00:02:11,360 –> 00:02:16,080 in the Bundestag.

    58 00:02:13,920 –> 00:02:18,360 So, only the Zweitstimme says

    59 00:02:16,080 –> 00:02:21,120 how many seats a party has in the parliament.

    60 00:02:18,360 –> 00:02:22,959 However, the people who can actually take the seats with priority

    61 00:02:21,120 –> 00:02:25,599 are the winners in the electoral districts.

    62 00:02:22,959 –> 00:02:27,480 It’s common that these candidates are

    63 00:02:25,599 –> 00:02:29,480 associated to political party as well.

    64 00:02:27,480 –> 00:02:30,760 This is not

    65 00:02:29,480 –> 00:02:32,360 a strong requirement but

    66 00:02:30,760 –> 00:02:34,120 it’s still the normal case.

    67 00:02:32,360 –> 00:02:36,519 In exceptional cases, it can happen

    68 00:02:34,120 –> 00:02:39,360 that an independent candidate

    69 00:02:36,519 –> 00:02:41,239 wins a given district.

    70 00:02:39,360 –> 00:02:43,319 In this case, this independent person immediately gets their seat in

    71 00:02:41,239 –> 00:02:46,080 the Bundestag. Everything that follows now does not hold for this person.

    72 00:02:43,319 –> 00:02:48,040 The winners that

    73 00:02:46,080 –> 00:02:50,159 are associated to a party

    74 00:02:48,040 –> 00:02:52,519 don’t get their seats immediately.

    75 00:02:50,159 –> 00:02:55,000 For them, it’s important

    76 00:02:52,519 –> 00:02:57,319 how many votes their part got with the Zweitstimme.

    77 00:02:55,000 –> 00:02:58,920 To make it clear again:

    78 00:02:57,319 –> 00:03:01,920 The winner of a district

    79 00:02:58,920 –> 00:03:04,080 is just the candidate that got the most

    80 00:03:01,920 –> 00:03:07,760 votes with the Erststimme.

    81 00:03:04,080 –> 00:03:10,319 So their is exactly one winner for each district.

    82 00:03:07,760 –> 00:03:11,920 However, if this winner associated to a party

    83 00:03:10,319 –> 00:03:14,159 really gets a seat in the parliament

    84 00:03:11,920 –> 00:03:16,640 is only decided by the amount of votes

    85 00:03:14,159 –> 00:03:18,840 in the Zweitstimme.

    86 00:03:16,640 –> 00:03:21,159 Let’s see how this works. After the election

    87 00:03:18,840 –> 00:03:24,040 we have the total number of valid votes in the Zweitstimmme.

    88 00:03:21,159 –> 00:03:27,519 This is done on the upper level, for the entire federation.

    89 00:03:24,040 –> 00:03:30,239 A common number in Germany is around 46 million votes.

    90 00:03:27,519 –> 00:03:32,040 And since the Zweitstimme can only be given

    91 00:03:30,239 –> 00:03:34,040 to a party,

    92 00:03:32,040 –> 00:03:35,680 we have a distribution of votes across all parties

    93 00:03:34,040 –> 00:03:37,799 that took part in the election.

    94 00:03:35,680 –> 00:03:40,319 So we just count the votes (Zweitstimmen)

    95 00:03:37,799 –> 00:03:42,840 and then we know how well a given

    96 00:03:40,319 –> 00:03:44,360 party has done.

    97 00:03:42,840 –> 00:03:46,480 Obviously, we can write this

    98 00:03:44,360 –> 00:03:48,879 as a percentage as well.

    99 00:03:46,480 –> 00:03:51,599 So we have the share of votes in relation

    100 00:03:48,879 –> 00:03:53,040 to the total number of valid votes.

    101 00:03:51,599 –> 00:03:54,920 On the other hand, we can also look

    102 00:03:53,040 –> 00:03:57,159 how successful the parties

    103 00:03:54,920 –> 00:03:59,000 were with respect to the Erststimme

    104 00:03:57,159 –> 00:04:01,640 This means how many of the 299 districts

    105 00:03:59,000 –> 00:04:04,120 they could win.

    106 00:04:01,640 –> 00:04:06,200 This is really important because now

    107 00:04:04,120 –> 00:04:09,120 it will be decided which party is

    108 00:04:06,200 –> 00:04:12,120 important enough for the Bundestag.

    109 00:04:09,120 –> 00:04:15,239 Unimportant are parties with less than 5% of the total second votes.

    110 00:04:12,120 –> 00:04:17,359 They will be thrown out completely unless

    111 00:04:15,239 –> 00:04:19,639 they have won at least three districts

    112 00:04:17,359 –> 00:04:22,479 with the Erststimme. In that case, they are spared.

    113 00:04:19,639 –> 00:04:24,800 So first check the 5% barrier and, if they are below, then check

    114 00:04:22,479 –> 00:04:29,240 how many districts are won.

    115 00:04:24,800 –> 00:04:31,840 For example, here 4.8% is not enough.

    116 00:04:29,240 –> 00:04:34,400 and two districts are also too little.

    117 00:04:31,840 –> 00:04:36,320 After these cancellations,

    118 00:04:34,400 –> 00:04:39,120 only some parties remain and exactly these

    119 00:04:36,320 –> 00:04:41,080 will get the seats in the parliament.

    120 00:04:39,120 –> 00:04:43,440 So we just have to find the correct number

    121 00:04:41,080 –> 00:04:45,960 and this is done with the so-called

    122 00:04:43,440 –> 00:04:47,440 Sainte-Laguë method/ Webster method.

    123 00:04:45,960 –> 00:04:49,039 I have a separate video for that

    124 00:04:47,440 –> 00:04:51,720 if you are interested in it.

    125 00:04:49,039 –> 00:04:53,800 Here, we can just apply it

    126 00:04:51,720 –> 00:04:56,560 and it’s only important to know

    127 00:04:53,800 –> 00:05:00,560 that the total number of seats in the Bundestag

    128 00:04:56,560 –> 00:05:02,800 is given by 630.

    129 00:05:00,560 –> 00:05:05,000 So with all the votes in Germany,

    130 00:05:02,800 –> 00:05:06,960 we find the suitable distribution of seats.

    131 00:05:05,000 –> 00:05:09,199 This distribution for the different parties is called “Oberverteilung”.

    132 00:05:06,960 –> 00:05:11,360 It already tells out the power of different parties

    133 00:05:09,199 –> 00:05:13,680 in the parliament.

    134 00:05:11,360 –> 00:05:15,759 However, we already know that

    135 00:05:13,680 –> 00:05:17,400 we need to put in more

    136 00:05:15,759 –> 00:05:20,160 because the votes (Zweitstimmen) were given

    137 00:05:17,400 –> 00:05:22,400 to a list in a state.

    138 00:05:20,160 –> 00:05:24,600 Hence, in the next step, we have to distribute

    139 00:05:22,400 –> 00:05:26,680 the seats to the 16 states.

    140 00:05:24,600 –> 00:05:28,440 This can be done for each party separately

    141 00:05:26,680 –> 00:05:30,240 since we know how many votes

    142 00:05:28,440 –> 00:05:32,360 each party got in each state.

    143 00:05:30,240 –> 00:05:34,560 Therefore, we just create a new list

    144 00:05:32,360 –> 00:05:36,919 where all 16 states are listed

    145 00:05:34,560 –> 00:05:39,360 with the corresponding number of votes

    146 00:05:36,919 –> 00:05:41,639 for the given party.

    147 00:05:39,360 –> 00:05:43,960 To this list, the Sainte-Laguë method is applied again.

    148 00:05:41,639 –> 00:05:46,680 Afterwards, each party knows

    149 00:05:43,960 –> 00:05:49,240 how many seats for each state

    150 00:05:46,680 –> 00:05:51,319 they get in the Bundestag.

    151 00:05:49,240 –> 00:05:53,840 Just to clarify: this second distribution

    152 00:05:51,319 –> 00:05:55,759 is often called “Unterverteilung”.

    153 00:05:53,840 –> 00:05:57,800 This distribution has to be calculated

    154 00:05:55,759 –> 00:06:00,400 for each (important) party.

    155 00:05:57,800 –> 00:06:02,840 With that, we also know the people who

    156 00:06:00,400 –> 00:06:05,120 will occupy the seats.

    157 00:06:02,840 –> 00:06:06,759 In order to see this, let’s jump

    158 00:06:05,120 –> 00:06:10,720 to one state, let’s say that this

    159 00:06:06,759 –> 00:06:12,720 is state 2 and we consider the party B.

    160 00:06:10,720 –> 00:06:15,440 So, we know that 8 seats can be given.

    161 00:06:12,720 –> 00:06:17,240 Please recall that, from the beginning,

    162 00:06:15,440 –> 00:06:19,199 the parties had lists of people in the states.

    163 00:06:17,240 –> 00:06:21,520 Indeed, this state list of the

    164 00:06:19,199 –> 00:06:23,599 given party is numbered consecutively

    165 00:06:21,520 –> 00:06:24,960 such that we can got step by step

    166 00:06:23,599 –> 00:06:26,880 to give the seats to different persons.

    167 00:06:24,960 –> 00:06:28,960 We can do this until all seats

    168 00:06:26,880 –> 00:06:31,160 are taken. However, actually some other people

    169 00:06:28,960 –> 00:06:33,680 have a higher priority first.

    170 00:06:31,160 –> 00:06:35,680 They are put on top of the list.

    171 00:06:33,680 –> 00:06:38,199 These are exactly the winners of the districts

    172 00:06:35,680 –> 00:06:41,000 that belong to the given state and party.

    173 00:06:38,199 –> 00:06:42,840 So people with the most votes (Erststimmen) in a district

    174 00:06:41,000 –> 00:06:44,759 are higher ranked than the state list.

    175 00:06:42,840 –> 00:06:46,639 Obviously, we only consider winners

    176 00:06:44,759 –> 00:06:49,440 that belong to party B. With that we

    177 00:06:46,639 –> 00:06:51,479 can order the whole list.

    178 00:06:49,440 –> 00:06:53,919 On top, we have the best winner. So the candidate that had the

    179 00:06:51,479 –> 00:06:55,560 highest percentage value in votes (Erststimmen).

    180 00:06:53,919 –> 00:06:57,479 Then comes the candidate with the next highest score.

    181 00:06:55,560 –> 00:07:00,120 And then it just goes on like this.

    182 00:06:57,479 –> 00:07:02,280 The list of priorities is done

    183 00:07:00,120 –> 00:07:04,520 and we can allocate the 8 seats.

    184 00:07:02,280 –> 00:07:06,639 At this point, you should see

    185 00:07:04,520 –> 00:07:08,360 that we have exactly 3 possibilities.

    186 00:07:06,639 –> 00:07:11,120 Let’s start with the best case.

    187 00:07:08,360 –> 00:07:13,360 There, all winners of the districts

    188 00:07:11,120 –> 00:07:16,280 take seats in the Bundestag.

    189 00:07:13,360 –> 00:07:18,479 And maybe also the first persons on the state list get seats.

    190 00:07:16,280 –> 00:07:20,960 In this case, it does not matter at all

    191 00:07:18,479 –> 00:07:23,240 how good a winner in a district actually was.

    192 00:07:20,960 –> 00:07:25,560 However, if there are too many winners

    193 00:07:23,240 –> 00:07:27,800 of the given party,

    194 00:07:25,560 –> 00:07:29,759 then it can definitely play an important role.

    195 00:07:27,800 –> 00:07:32,120 In this case, the worst winners

    196 00:07:29,759 –> 00:07:34,520 will not get a seat in the Bundestag.

    197 00:07:32,120 –> 00:07:36,520 There are simply not enough seats for the party

    198 00:07:34,520 –> 00:07:38,800 and in this case, the state list is also

    199 00:07:36,520 –> 00:07:41,039 untouched.

    200 00:07:38,800 –> 00:07:43,160 Now, the third case is something that

    201 00:07:41,039 –> 00:07:45,960 actually should never happen, but theoretically, it’s possible.

    202 00:07:43,160 –> 00:07:47,720 It could happen that the state list

    203 00:07:45,960 –> 00:07:50,159 is too short, meaning that the party

    204 00:07:47,720 –> 00:07:52,319 did not find enough people to put on the list

    205 00:07:50,159 –> 00:07:54,120 and now they can’t fill all their seats.

    206 00:07:52,319 –> 00:07:57,400 Therefore, these seats will just stay empty

    207 00:07:54,120 –> 00:07:59,599 and they remain unoccupied in the Bundestag

    208 00:07:57,400 –> 00:08:01,639 Hence, only if such a case occurs,

    209 00:07:59,599 –> 00:08:04,639 can the total number of seats

    210 00:08:01,639 –> 00:08:06,039 in the parliament be smaller than 630.

    211 00:08:04,639 –> 00:08:07,800 In fact, on the other hand, there is still

    212 00:08:06,039 –> 00:08:11,120 a special case that the total number is greater

    213 00:08:07,800 –> 00:08:12,879 than the planned 630.

    214 00:08:11,120 –> 00:08:16,720 This can only happen if a party

    215 00:08:12,879 –> 00:08:19,599 get more than 50% of the

    216 00:08:16,720 –> 00:08:21,599 relevant second votes (Zweitstimmen).

    217 00:08:19,599 –> 00:08:23,680 Then this party must get more than

    218 00:08:21,599 –> 00:08:25,360 50% of the seats in the parliament.

    219 00:08:23,680 –> 00:08:27,400 Because of rounding errors

    220 00:08:25,360 –> 00:08:29,120 during the distribution procedure,

    221 00:08:27,400 –> 00:08:31,520 this is not guaranteed.

    222 00:08:29,120 –> 00:08:32,680 Hence, one has to add seats until

    223 00:08:31,520 –> 00:08:36,320 until 50% are exceeded.

    224 00:08:32,680 –> 00:08:37,800 For the election 2025 this is not expected.

    225 00:08:36,320 –> 00:08:39,959 I now hope that this voting procedure is clearer and

    226 00:08:37,800 –> 00:08:41,640 that there will be no more confusion

    227 00:08:39,959 –> 00:08:43,959 when you have the ballot paper in front of you.

    228 00:08:41,640 –> 00:08:45,880 Otherwise we can discuss further

    229 00:08:43,959 –> 00:08:48,240 questions in the comments.

    230 00:08:45,880 –> 00:08:50,380 See you next time.

    231 00:08:48,240 –> 00:09:00,560 Bye!

    232 00:08:50,380 –> 00:09:03,560 [Musik]

    233 00:09:00,560 –> 00:09:03,560 of

    234 00:09:05,230 –> 00:09:08,850 [Musik]

  • Quiz Content (n/a)
  • Date of video: 2024-12-17

  • Back to overview page


Do you search for another mathematical topic?