Votes2Seats in Germany
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partysourcenation-wideBaden-WBayernBerlinBrandenb.BremenHamburgHessenMeck.-V.Nieders.Nordr.-W.R.-PfalzSaarlandSachsenSachsen-A.S.-Holst.Thüringen
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How does Germany calculate parliament seats from absolute votes?
A spreadsheet essay, meaning you can click on each cell to understand the calculation. By @lisacrost.
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Disclaimer 1: You'll need some basic knowledge of the German voting system to follow this essay. Super-short eplanation: With the ERSTSTIMME (=first vote), voters vote one representative (often affiliated with a party) of their election district into parliament. With the ZWEISTIMME (=second vote), voters vote for a party and therefore decide how many seats each party should get in parliament.

Disclaimer 2: Don't trust these numbers. It's a rough calculation to show the basics. If you are a government and clueless how to deal with all the votes you gathered in your last election, please consult an expert.

Mistakes? Ideas to improve the understanding? Please: lisacharlotterost@gmail.com
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1. The Basics, to get started.
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Hi! Here are some facts about the 2013 election, which we'll take as an example to show the calculation from votes to parliament seats. eligible votershttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf61946900768989594727382505718206594448382312819184413271135070561174731325355430924247960723406430193088022517961834259
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votershttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf44309925571146966337261815415141278533302290121332304838817184491281960524722519795774282368758119824816457501251403
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turnout in %calculated71.574.370.072.568.468.870.373.265.373.472.572.872.569.562.173.168.2
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valid ZWEITSTIMMENhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf43726856564201965807551787721138836232941289082931480918677434445260949815722144975625602332652117881516282901231693
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To understand how the election results result in parliament seats, we need election results. Here is the absolute number of ZWEITSTIMME voters for each party and each state. We'll use that to calculate things below.CDUhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf14921877257660650864348260196459285927123299436904818255923776563958655212368994601485781638756477283
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SPDhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf112522151160424131400943938732117411720428890290690615443114700053028282608910174592340819214731513725198714
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DIE LINKEhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf375569927245624892033050731131233284782961886541868712239355829251203385604546704528231984177288615
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GRÜNEhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf3694057623294552818220737651824001411282631313537716391901760642169372319981139164685815313760511
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CSUhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf32435693243569
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Here are the voting percentages for the ZWEITSTIMME for each party in each state. Since we'll use the absolute voters, these numbers are just for orientation.CDUcalculated34.145.728.534.829.332.139.242.541.139.843.337.842.641.239.238.8
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SPDcalculated25.720.620.024.623.135.632.428.817.833.131.927.531.014.618.231.516.1
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DIE LINKEcalculated8.64.83.818.522.410.18.86.021.55.06.15.410.020.023.95.223.4
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GRÜNEcalculated8.411.08.412.34.712.112.79.94.38.88.07.65.74.94.09.44.9
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CSUcalculated7.449.3
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Because of the election threshold, only the parties with more than 5% of the votes get into parliament and get our attention. Here we calculate the sum of voters of the parties who did get into parliament. We'll need it later.CDU+SPD+LINKE+GRÜNE+CSUcalculated36867417463278053593161499274118026928696176595126416897480663911433814841218572754750031916381102968913897951025123
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The German parliament offers 598 seats to fill, and it's easy to figure out how many seats per state can be allocated to each party: For approx. every 124k inhabitants, each state gets one parliament seat to fill.inhabitanshttps://www.bundeswahlleiter.de/mitteilungen/bundestagswahl-2013/20130902-sitzkontingente.html74.59482902113532643025288241826757580515596555388350158503273548921589518236728889194024005278224767326860852154202
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seatscalculated5987692241951343135912830732182217
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2. Oh No: Statewide ZWEITSTIMME Seats vs. Nationwide ZWEISTIMME Seats Result in Overhang Mandates 😱
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To find out the number of seats per party per state, let's look at the ZWEITSTIMME first. Here we calculate the number of seats that every party in each state should get according to the ZWEITSTIMME. To do so, we first divide the total number of big-party-voters by the number of seats, answering the question: How many voters decided one seat in the whole state? Then we'll see how often that number of one-seat-voters fits into the number of voters for each party. And voila, we get the number of seats that each party deserves.CDUcalculated23942088252062859153178108
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SPDcalculated1831923752515322481036483
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DIE LINKEcalculated604455113339218515
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GRÜNEcalculated60109411251612302121
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CSUcalculated5605600000000000000
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total seatscalculated5980000000000000000
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But surprisingly, we're running into a problem here. Let me explain. Here we calculate how many seats the parties should have on a national level, if we just take into account the number of seats (598) and allocate them on the parties according to their relative ZWEITSTIMME votes.CDUcalculated242
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SPDcalculated183
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DIE LINKEcalculated61
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GRÜNEcalculated60
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CSUcalculated53
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Then we check if one of the parties deserves more seats according to the ZWEITSTIMME then it does according to the relative values. Here we see that the CSU actually earned 56 seats, but according to the seat allocation based on relative values, it should only have 53 seats. This difference is called overhang mandates. Argh! We'll handle this later.CDUcalculated-3
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SPDcalculated0
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DIE LINKEcalculated-1
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GRÜNEcalculated0
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CSUcalculated3
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3. Oh No, Again: Statewide ZWEITSTIMME Seats vs. Statewide ERSTSTIMME Seats Result in Even More Overhang Mandates 😱
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So far we've only looked at the ZWEISTIMME results. Let's change that. Here we can see which party earned how many election districts (and therefore seats) with their ERSTSTIMME in which state.CDUhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf19138591176173714416999
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SPDhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf5821255132712
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DIE LINKEhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf44
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GRÜNEhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf11
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CSUhttps://www.bundeswahlleiter.de/dam/jcr/a832ae2d-3ffc-4805-92c6-c92cc8668d17/btw13_heft3.pdf4545
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totalcalculated29938451210262263064154169119
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In most states, parties earn far more seats with their ZWEISTIMME than they earn election district seats. But we can see that in four states, the CDU won more election districts than they won seats through the ZWEITSTIMME. Yay, another problem!CDUcalculated43-1243011221-11-11-1
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SPDcalculated19235400103921936463
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DIE LINKEcalculated4415113339218515
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GRÜNEcalculated109311251612302121
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CSUcalculated11
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These extra seats are also overhang mandates.CDUcalculated4
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SPDcalculated0
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DIE LINKEcalculated0
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GRÜNEcalculated0
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CSUcalculated0
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4. The Solution to Both Problems
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Here, we put everything together. These are the minimum parliament seats that every party deserves after calculating the overhang mandates from the two problems. We see that in this list, the CSU has its deserved 56 seats (instead of 53) and the CDU has its deserved 243 seats (instead of 239).CDUcalculated243
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SPDcalculated183
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DIE LINKEcalculated60
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GRÜNEcalculated60
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CSUcalculated56
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totalcalculated602
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But these can't be the final seats, because another condition needs to be considered: Every party should have seats according to the relative ZWEITSTIMME votes. Here we can see the difference between the percentage of minimum parliament seats and the voting percentage of ZWEITSTIMMEN. We can see that the CSU gains a lot of relative power (it is as if 0.5% more Bavarian voters had voted for the CSU) at the cost of other parties. That's not fair to the other parties.CDUcalculated-0.1
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SPDcalculated-0.1
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DIE LINKEcalculated-0.2
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GRÜNEcalculated-0.1
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CSUcalculated0.5
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How can we make it fair? By making all seats worth the same number of voters. To do so, we're checking how much CSU votes were needed to earn one of these 56 CSU seats (I admit: I have no idea why I need to substract 0.5 from the CSU voters in the calculation). Turns out, it's something around 58k voters. Now we're dividing the number of voters for each party (nationwide) by these 58k voters. That gives us a parliament in which each seat was determined by the same amount of voters. divisorcalculated according to http://www.wahlrecht.de/news/2013/2013100901.html58443
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CDUcalculated255
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SPDcalculated193
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DIE LINKEcalculated64
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GRÜNEcalculated63
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CSUcalculated56
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The disadvantage of this method: The parliament grows like crazy. Now we're up to 631 seats instead of the normal 598 seats. totalcalculated631
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5. The Grand Finale: Seats on State Level
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So now we know the number of seats each party gets! But what's the number of seats each party gets on the state level? Easy peasy. Calculating the seats on the state level is very similar to calculating them on the national level. Here too, we try to understand how many voters were necessary for one seat – but for each party seperately. Turns out, for each CSU seat in 2013, only 57.9k voters were needed, while for one Green seat, 58.6k voters were necessary.CDUcalculated58517.16
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SPDcalculated58301.63
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DIE LINKEcalculated58682.80
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GRÜNEcalculated58635.83
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CSUcalculated57920.88
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