How the German overhang and compensation system works

Heinz Brandenburg on Twitter walks readers through a very useful explainer on how the current Germany version of MMP deals with overhangs through a multi-layered compensation mechanism, and why it could mean the new Bundestag will top out at more than 800 seats!

It is best to read it in its native Twitter, but following is the text of most of it (courtesy of the ThreadReader app) . The starting point, not quoted here, is a poll of current party standing in the state of Bavaria.

[the remainder of this text is not mine, but Brandenburg’s; numbers correspond to tweets in the thread]

____________________________________________________________________________

Last time around, the CSU won 38.8% of the vote but all of the constituencies in Bavaria (they even swept all of Munich). That results in so-called overhang and compensatory seats.
How are these calculated?

1/ Well, there are 93 regular seats allocated to Bavaria, 46 of which are constituencies. CSU winning them all meant 46 seats, but they only had 38.8% of the list vote or about 42% of the vote once you discount votes for parties that did not get into the Bundestag.

2/ 42% of the vote would mean their proportional share of seats was 39, not 46. So they got 7 Ueberhangmandate (overhang seats), i.e. 7 more seats than their proportional share.

3/ Since 2013, these seats have to be compensated for. So other parties get additional seats, to the extent that the 46 seats the CSU won amount to 42% of the total number of seats in Bavaria.
So Bavaria actually had 108 seats in the Bundestag, not 93. 

4/ But that is not the end of it. Bavaria’s 93 seats are proportional to its population size. If the state’s seat share increases to 108, then the 15 other states also need a larger share. And it wasn’t only Bavaria. 

5/ Baden-Wuerttemberg got 96 instead of 76 because of the CDU winning all constituencies, Brandenburg 25 instead of 20 because CDU won all but one constituency, Hamburg 16 instead of 12 because SPD won all but one constituency, and so on.

6/ What happens then is that to keep the 16 states’ share of seats in the Bundestag proportional, not only overhang seats within states need to be compensated, but overhang and compensatory seats within states have to be compensated across states.

7/ So North Rhine-Westphalia (NRW), the biggest German state, did not produce any overhang seats, because SPD and CDU are more evenly balanced there. But it got 14 compensatory seats, to make up for additional seats given to other states. 

8/ It is not a perfect compensation across states. Bavaria and Baden-Wuerttemberg have 15 and 20 seats, respectively, more than their normal share in the 2017 Bundestag. NRW only 14, despite being the larger state.

9/ Berlin, Niedersachsen and NRW were the only states where no overhang seats were dished out in 2017, largely a reflection of dominance of the CDU in a fragmenting party landscape. 

10/ CDU won all seats in five states, almost all seats in over a dozen states, despite having their worst election result in history, with 33%.

Could be very different this time around, with them down to 20% and the SPD at 25%. More states could get away without overhang seats.

11/ But one single state can make a big difference, and if the result in Bavaria is anywhere close to the recent polls (CSU 28%) it could be a dramatic effect.

12/ Even at 28%, the CSU would like win almost all constituencies. These are the four most marginal seats. Muenchen-Nord and Nuernberg-Nord are most likely to fall to the SPD. But the others are not certain.

So the CSU could still end up with 42-44 seats, on just 28% of the vote, or 31% if we remove votes for parties that do not get into the Bundestag.

14/ By my calculations, that would mean Bavaria’s seat share increases to 129 seats from their current 108 (and their nominal allocation of 93).

Once other states are compensated, that would get us to possibly 840 seats. 

15/ A few changes have been made, which I have taken into account – the first three overhang seats will not be compensated, which would keep Bavaria’s share at 129 rather than 135 under 2017 rules.

16/ And overhangs can also be compensated against a party’s list seats in other states. But I don’t think that applies to the CSU. They won’t take CDU seats away in other states to compensate for CSU over-representations.

17/ So one such lop-sided result, under increasing fragmentation – where suddenly 28% of the vote share allow a party to win almost all constituencies – can have incredible effects on the size of the Bundestag.

18/ The nominal size of the Bundestag is 598. This one result in Bavaria could increase the size of parliament by 40%.

24 thoughts on “How the German overhang and compensation system works

  1. Okay, maybe I am missing something here but does this mean Germany could get away with fewer overhang seats if they were used only to ensure proportionality nationwide among parties, and not among Laender?
    I used to think Laender needed proportionate numbers of Bundestag seats (list seats as well as constituencies) to determine how many electors each Landtag got to appoint in federal presidential elections – analogous to the US Electoral College if only House seats counted – but it seems that Germany reallocates electoral votes among States based on populations at the time of the presidential election, not based on Bundestag seats from the last parliamentary election.

    • Yes, if you just took away the initial Land-by-Land calculation and distributed seats nationally, it would probably limit just how big the Bundestag gets, although treating the CSU as if they’re a separate party and not a state branch of the CDU (yes, I know they’re legally two separate entities) will always complicate that so long as the CSU continues to dominate the nominal tier even as their list tier vote dwindles.

      The ironic thing is that the final calculation doesn’t even result in overall proportionality either by Land population or by votes cast in each Land, as the overhand in a given Land remains and as votes are distributed proportionately to Land lists within a party, so rounding could see certain Laender ending up with a disproportionate share of seats.

      • By 2050, all employment-age Germans will either be a member of the Bundestag or advising a committee on how to adjust MMP to reduce the number of members of the Bundestag.

      • This may be the least comprehensible electoral system I have laid my eyes on.

      • The article by Dr. Pukelsheim and Dr. Bischof is very informative, but my lack of fluency in German made it hard to grasp some of the finer points of the recently amended Bundestag election law. Fortunately, the article included a link to a page on the Federal Returning Officer’s website, which has a step-by-step notional distribution of Bundestag seats in the 2017 general election under the new system, which clarified many of the doubts I had.

        I’ll have more to say about the matter later, but for the time being suffice it to be said that the article’s authors were right on target when they stated that “the transition from the 2013 Bundestag election law to the 2020 Bundestag election law leads from bad to worse.”

      • As I noted yesterday, Germany’s Federal Returning Officer’s website has a step-by-step notional allocation of Bundestag seats in the 2017 general election under the amended electoral law, available here in PDF format. The site also has the English-language version of the Federal Elections Act, also in PDF format, but it’s fairly dense legal language.

        At any rate, the Federal Elections Act continues to provide for an initial, non-binding allocation of seats among qualifying parties, carried out in each one of Germany’s sixteen Länder by the Sainte-Laguë/Schepers method of PR. However, and unlike in 2013 and 2017, if a party secures more constituency seats in the first vote of a particular Land than the number of seats it would be entitled to according to the result of the second vote, the extra seats are not factored in at this stage. Instead, the non-binding allocation seat totals obtained by each qualifying party at the Land level are added up to obtain the following nationwide totals: 164 CDU, 131 SPD, 59 DIE LINKE, 57 GRÜNE, 39 CSU, 65 FDP and 83 AfD.

        Meanwhile, in each Land a minimum amount of seats is determined for every qualifying party. That figure is equal to the larger of the number of constituency seats won by the party, or the rounded average of the party’s constituency and overall seat totals from the initial non-binding allocation. The minimums determined for each qualifying party at the Land level are also added up, producing the following nationwide totals: 194 CDU, 101 SPD, 35 DIE LINKE, 33 GRÜNE, 46 CSU, 38 FDP and 47 AfD. Moreover, when a party wins more constituency mandates in the first vote of a particular Land than the number of seats it would be entitled to according to the non-binding allocation of seats, the difference between both figures is treated as a potential overhang, and these are added up as well, producing these nationwide totals: CDU 36, SPD 3 and CSU 7.

        After these calculations are carried out, a nationwide seat minimum is determined for each qualifying party; that figure is equal to the larger of the nationwide sum of its Land seat minimums, or its nationwide non-binding seat allocation total. For the seven qualifying parties, the nationwide seat minimums would be as follows: 194 CDU, 131 SPD, 59 DIE LINKE, 57 GRÜNE, 46 CSU, 65 FDP and 83 AfD. Then, a Sainte-Laguë allocation divisor is determined such that each qualifying party without potential overhang mandates will receive a total number of mandates equal to or larger than its nationwide seat minimum, while the qualifying party or parties with potential overhang mandates receive each a number of seats such that all of them do not have more than three overhang mandates. In other words, the sum of differences between the seat totals obtained by parties with overhang mandates and their respective nationwide seat minimums should not exceed three.

        For the 2017 Bundestag election, a divisor of 64,660 would have satisfied the listed requirements, producing the following seat distribution: 193 CDU, 148 SPD, 66 DIE LINKE, 64 GRÜNE, 44 CSU, 77 FDP and 91 AfD, for a total of 683 seats. Then, CDU and CSU would be brought up to their respective nationwide seat minimums of 194 and 46, for a grand total of 686 seats with the single CDU and two CSU overhang mandates.

        Under the current Elections Act, the allocation of Bundestag seats at the federal level remains definitive and cannot be altered by the distribution of party mandates at the Land level. As such, in the event one or more party Land lists receive fewer seats than the corresponding minimum number of seats determined for the party, the allocation divisor would be increased until each one of the party’s Land lists received a number of seats equal to or larger than its corresponding seat minimum. If a party has overhang mandates, the votes obtained by its Land lists with potential overhang mandates are divided by the number of assigned seats minus 0.5, 1.5 and 2.5; overhang mandates are assigned to the party’s Land list(s) with the lowest quotient(s); this procedure would be moot in the case of CSU’s two overhang mandates, since the party ran only in Bavaria.

        In all, a handful of overhang mandates – up to three – and a very small deviation from full proportionality are allowed once more, in order to contain the expansion of the Bundestag, which in 2017 would have had 23 fewer seats than it did under the terms of the 2013 Federal Elections Act. However, in the process Germany has come up with one of the world’s most complicated electoral systems (albeit in all fairness the calculations to determine the nationwide distribution of Bundestag seats can be carried out with relative ease in a spreadsheet program). Moreover, simulations of Bundestag seat distributions for general elections prior to 2017 show that in some instances, such as 2013, the revised system would produce a Bundestag with the same amount of seats as the 2013 Elections Act.

        In fact, a simulation of 2017 Bundestag election results using the second vote to determine constituency seat winners – as if there had been no separate first vote in place, with the results of the single vote identical to those of the actual second vote – shows that under the current Elections Act, the Bundestag would have had a total of 737 seats, or just seven fewer than 744 under the 2013 Elections Act; the increase of the size of the Bundestag in either case would have been largely due to CDU winning in 210 of 299 constituencies (and CSU 46), to just 29 for SPD and seven each for DIE LINKE and AfD. On the other hand, a simulation of full 2009 general election results indicates that under the current Elections Act, the Bundestag would have had 636 seats, as opposed to 671 under the 2013 Elections Act.

        At the end of the day, the problem lies with the votes-to-seats distortions introduced in single-member constituencies by FPTP, with its potential to deliver lopsided majorities to low-plurality winners, both nationwide and regionally (e.g. CSU in Bavaria) under an increasingly fragmented political landscape – which in turn require large seat expansions of the Bundestag in order to offset such distortions, attain fully or near-fully proportional seat distributions among qualifying parties, and most importantly comply with past Constitutional Court rulings. Time will tell whether or not the changes introduced by the current Elections Act prove to be nothing more than a short-term fix, and a very complicated one at that.

    • The disadvantages of MMP is too many overhang seats can result from winning too many single member district plurality and decoy lists can impact this greatly, but not an issue in Germany and New Zealand.

      Is a 50/50 ratio of SMD/List work or 40/60 ratio of SMD/List reduce overhangs?

      Wouldn’t Germany be better off to have the list seats for one district for the whole country like New Zealand rather than allocating to the 16 Länder? Does
      this method make overhangs more or less likely?

      • Rob, I suppose the objection to a single national compensation district is it would run against the grain of federalism. But I am not sufficiently familiar with the debates in Germany on this to know how vigorously this issue is raised.

    • I am not sure what you might mean by that, as each Scandinavian country has its own distinctive PR model. They are all (variations of) compensatory two-tier PR, so perhaps that is what you mean.

  2. I am delighted and hopeful that the German MMP system falling apart at the seams will discourage any future attempt in other countries to switch to this deeply flawed proportional system that has potentially catastrophic consequences that can shake the confidence of voters and requires ever more complicated fixes.

    • I would hardly call having a larger legislature “falling apart at the seams.” They seem to be quite functional despite the large assembly.

      It would be quite easy to fix the problem with German MMP without a massive increase in seats: determine the party with the lowest vote per seat ratio after awarding the SMDs, and distribute seats to the remaining parties so that they have the same ratio of votes per seat. After doing this, if there are fewer than 598 MPs (MBs? not sure what one calls a member of the Bundestag), distribute the remaining seats using the PR formula of your choice.

      • The abbreviation used in German is ‘MdB’, for “Mitglied des Bundestages” (i.e. Member of the Bundestag). The plural would still be ‘MdB’.

    • John, the issue of expansion of the assembly is not inherent to MMP. The current problem is the failure of the political parties to agree on a fix to the problems generated by a Constitutional Court ruling several years back. It is all fixable, in principle, and abolishing MMP.

      • I have seen “MdB” used in an English-language publication, but only once… by Professor Leslie Sykes in his 1990 pamphlet “Proportional Representation: Which System?” https://www.theguardian.com/news/2001/apr/16/guardianobituaries.education.
        which was memorable for the two grounds on which Professor Sykes favoured MMP and dismissed STV:
        (a) STV gives you only a paltry (like it says on the biscuit tin) “single” vote, whereas when filling, say, five seats, your natural expectation would be that you would be accorded a whole five (count ’em, five (5)) votes.
        (b) Moreover, STV is far less proportional than MMP, because it uses paltry five-seat constituencies instead of a wonderfully super-proportional nation-wide 498-seat constituency (for parties/ seats purposes) as in Germany.
        It was a privately-published pamphlet, in case you’re scratching your head wondering how that slipped past the editor. But Prof Sykes (who was a professor of French) did know his German.

  3. MSS is right. One can have an MMP system without overhang seats. Scotland has managed this for two decades. You don’t need to go further and retroactively re-defeat enough constituency winners to reduce an overhang party to its proportionate share of seats. It also gives some incentive for parties to win local districts rather than relying solely on the (usually but not invariably closed) lists to make up their parliamentary numbers.
    I don’t, myself, consider plurality winners in single-seat districts to have much more of a “personal mandate” than names on a party list – the idea that, because there is only one name on the ballot per party, some decisive proportion of voters carefully peruse that individual’s personal qualities seems to have little application outside by-elections and a few marginals. Enid Lakeman’s dismissal of plurality as “in fact, a party list with one name only” is snarky but accurate. But it is a social fact that people who are attracted to MMP, and/or wary of multi-member candidate contests, place great weight on “We promise that your vote for this candidate goes only to this candidate and cannot help elect someone else from the same party” even if they seem to skim over the correlative “Unfortunately, old chap, you can only vote for this candidate even if you would prefer to elect someone else from the same party”.

    • “People who are attracted to MMP place great weight on “We promise that your vote for this candidate goes only to this candidate and cannot help elect someone else from the same party” even if they seem to skim over the correlative “Unfortunately, old chap, you can only vote for this candidate even if you would prefer to elect someone else from the same party”. Not so, with the open-list variation recommended by the Law Commission of Canada. Assuming most of the regional candidates for top-up seats are also local candidates as found in Germany, one can easily split one’s ballot (32% in New Zealand do so), vote for a competing local candidate you prefer as a person, and vote for a nearby regional candidate of your party who you want to elect. Problem solved.

    • I would push back on the idea that one can have MMP without compensating for overhang seats.

      The Scottish results are not proportional precisely because they don’t compensate for them. In May’s election the SNP won more list seats than pure d’Hondt would have given them in 5 regions and two seats more than d’Hondt in a sixth region.

      Overall they won 49.6% of seats on just 42.5% of the vote for parties that earned at least one seat. That’s not proportional. It’s more proportional than FPTP or parallel systems, but the SNP has a near-parliamentary majority solely because of the overhang.

      • I will push right back! The P need not stand for purist. We generally consider Spain and several other countries with PR allocation rules to be “proportional” systems, even though their design (moderate magnitude, D’Hondt, etc.) makes them often short of full proportionality. So we can for MMP that does not deliver perfect proportionality. In fact, one could argue–not saying it is necessarily my argument–that the MM notion implies that there should be some reward for a party that is strong in the districts, and so if a party ends up somewhat above its proportional entitlement, that is inherent in the design. “Best of both worlds” and all that.

      • I concur with MSS, and recent developments in Germany should serve as a cautionary lesson against purism in that regard, all the more so with a FPTP component capable of potentially enormous votes-to-seats distorting effects. In fact, Germany has had to move (slightly) away from pure PR and allow a small number of overhang seats, in an attempt to contain the uncontrolled growth of the Bundestag.

        Much like in “The Sorcerer’s Apprentice,” German lawmakers thought they had come with the perfect spell for full PR, only to find out later on that it’s flooding the Bundestag with hundreds of additional members, and that attempts to (partially) undo the spell prove ineffective. As such, the ending appears quite predictable: like the sorcerer in the story, Karlsruhe will have to step in and sort out the mess.

    • I did not know Lakeman had made that comment about FPTP being a party list with only one name. That point is central to some key arguments in both Votes from Seats and Party Personnel Strategies. Once again, an idea I thought I had come up with turns out to be unoriginal!

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