The Bundestag uses a version of the Additional Members System - with some differences to the Scottish version - and there is a national 5% threshhold.
Basically (and there is one exception), if a party fails to get 5% of the vote, then it fails to get any "top-up" seats. When the votes have been counted, the regional votes of all the qualifying parties (i.e. those entitled to list seats) are totted up for each Land and the number of seats a party is entitled to in that Land is calculated as if all of that Land's seats were allocated that way.
This may sound confusing, so look at a local example. The Scottish Parliament is elected using AMS, and the d'Hondt method is used for allocating the "top-up" seats, which is a slightly different allocation method to the German one, but stick with this example.
Mid Scotland & Fife returns 16 Members of the Scottish Parliament - with there being 9 constituencies and 7 "top-up" members. If we used d'Hondt to allocate all 16, then we would get:
If we followed a Germanic method, then we would deduct the number of constituencies (8 SNP, 1 Labour) to get the number of "top-up" seats a party is entitled to:
Which is exactly the real situation.
The Bundestag was set up with the idea that half the seats would be constituencies, and half would be top-up, so with 299 constituencies, we should expect there to be 598 seats. At the September 2009 election, the result was:
So, we see 299 elected on constituencies, and 323 elected as "top-up" members. Has something gone wrong with the maths?
Look at another Scottish example - this time Lothian. This is unusual as the only region where the SNP did not win any "top-up" seats, and so the good people of Edinburgh Northern & Leith are the only people in Scotland not to have an SNP MSP.
If we follow the same method that we did for Mid Scotland & Fife, then we find the parties are entitled to the following number of seats:
Subtract the number of constituencies (8 SNP, 1 Labour) and the number of "top-up" seats each party would be entitled to is:
How do we deal with the SNP? We could, perhaps, take their most marginal constituency in this region, Edinburgh Central, and award that to the second-place Labour, and reduce the number of "top-up" seats that Labour is entitled to to 2.
Now, the system of AMS used in Scotland never encounters this sort of problem as it is an additive system - after the constituencies have been awarded, it is then worked out how many "top-up" seats a party should be given.
The Bundestag has a subtractive system - the number of seats in a Land which a party is entitled to is worked out, then the number of constituencies subtracted to work out how many "top-up" seats should be awarded. And that creates "overhang" seats in some Länder whereby a party gains more constituencies than it would be entitled to on a proportional system.
As a result, the Bundestag is enlarged by 24 seats beyond its expected 598 members.
As a rough guide, on a pure system, where there are no overhang seats and the seats are allocated in proportion of the national vote at a national level, we would get:
The use of overhang seats has increased the CDU/CSU-FDP majority from 18 to 42.
With 14.56% of the vote, the FDP got their best-ever result. For the past 20 years or so, in the run-up to elections, there has often been speculation that they would fall below that 5% threshhold and crash out of the Bundestag.
And one thing that saves them is supporters of their coalition partners giving them their second votes. If you support a main party and live in a Land where your party is likely to get overhang seats, then that means it won't get any "top-up" seats there, so it is logical to give your second vote to your party's junior partner.
But there is another reason for voting tactically to keep your partner above the 5% threshhold. Now, suppose that the total CDU/CSU-FDP vote remains the same, but the FDP gets one vote less than that 5% threshhold. We then get:
Good news for the CDU/CSU as its share of the vote and number of seats soars? Not really. The Left cannot be touched with a bargepole, a CDU/CSU-Green coalition is unlikely, leaving the only majority coalition possible a grand one of the CDU/CSU with the SPD.
Yes, Angela Merkel gets a third term as Chancellor, but not leading the Government of her choice.
Next, increase the FDP vote by one, at the expense of the CDU/CSU, so the FDP just hits that 5% threshhold:
This would give a CDU/CSU-FDP majority of 18 again.
Hence, the 5% threshhold rule creates an interesting effect that you if you support one of the 2 main parties, you can help them by voting against them.