The German voting system for the federal legislature (Bundestag) is a complete mess, and I would strongly advise any other country against introducing it. It is ridiculously complicated, and the main reason for this is that the Constitutional Court keeps interfering with it. Each ruling of the Court attempted to fix one perceived shortcoming of the system but then introduced another.
The basic idea of the system is the following:
It tries to combine PR with single-member constituencies (districts). The target size of the Bundestag is 598, and there exist half as many seats as that (299). This does not mean, however, that half the seats are allocated in single-member constituencies and the other half via PR; the process is more complicated than that, which I will describe below.
Each voter has two votes that operate separately. The first vote is for an individual candidate in the constituency of residence. The second vote is for a party list; Germany consists of sixteen states, and the parties draw up a list in each state. This second vote is for the purposes of PR: After the election, the second votes are tallied nationwide and determine the overall number of seats a party is getting, disregarding those parties that have less than 5 % nationwide (because we don’t want small parties in parliament). In a second step, this nationwide allocation of seats is then broken down along the lines of the sixteen state lists of that party to fill up those seats not yet won via the constituencies from the state lists.
So imagine, for instance, a party getting 10 % of the nationwide vote, which ought to get it 59 or 60 (based on the exact figures) seats in parliament. Let’s say it comes down to 59. These 59 seats are then allocated to the sixteen state lists of that party, on the basis of how much the second votes won by the party in that state make up as part of its nationwide total, so the share of the party in state X might amount to, say, ten seats. If the party won eight constituencies in that state, then the first two candidates of the party list in that state would be considered elected in addition to the eight successful district candidates. So far so good.
But here is already potential for things to get messy. Suppose the party won more constituencies in that state than its seat share under PR; in our example, let’s say they won twelve constituencies in the state, but the PR share of the state list of that party is still ten. Under the old law, the rules would say that all these twelve constituency candidates are elected (they won their district fair and square, after all), so the party gets to keep those twelve seats despite having won only ten under the rules of PR.
But now the overall size of the legislature has grown from 598 to 600 by those extra two seats that the party gets to keep, an effect known as Überhangmandate (excess seats) in German.
But now things get more complicated again. The Constitutional Court, in its infinite wisdom, interprets the (very vague wording of the) constitution as saying that the relative shares of parties in parliament must be in accordance with the shares of second votes won, and excess seats destroy this. So the law compensates for the excess seats by giving yet more seats to the other parties (other than the one that won the excess seats) so that the relative shares of seats of all parties corresponds to the relative shares of second votes won. These additional seats are known as Ausgleichsmandate (compensation seats).
The cumulative effect of excess and compensation seats means that the current Bundestag has a whopping 733 members in total rather than the target size of 598.
But there is also potential for things to get really absurd. Consider the lists of the same party in states X and Y. Perhaps the party won ten PR seats in state X and seven in state Y. But imagine a counterfactual where the party had gained just a few votes more in state X than it really has, and that this would have meant that at the step of allocating the nationwide PR seats to state lists, one of the PR seats in state Y would move to state X (so that the state list in state X would get eleven seats instead of ten, and the state list in Y six instead of seven). The total PR seats won at the national level would not change. But the additional PR seat in state X is worthless because the party already has twelve seats in that state; there’s no difference whether the PR seats allocated to that state are ten or eleven. But perhaps the PR seats for that party make a difference in state Y, where the party won fewer constituencies than PR seats. The consequence of this is that there can be situations where a party would have got more total seats nationwide if it had received a few votes less in a given state, a phenomenon known as negative effect of votes (negatives Stimmgewicht in German). This problem is still unresolved
In 2023, federal legislators got tired of inflating parliament with excess and compensation seats and decided to fix the size of the Bundestag at an unalterable 630. But the basic voting system remains the same. This means that under the new rules (which will first be applied in the 2025 elections), it is possible that someone wins the election in a constituency and will still not enter parliament, if the party already has too many constituency seats in that state compared to its share of second votes. This makes a complete mockery of the democratic decision of the voters in that district, and it will intensify a phenomenon that is already strong in Germany, namely, that the parties consider seats owned by them rather than won by cnadidates (with the resulting effect that members of the Bundestag tend to be less independently minded relative to their party leadership than their colleagues in other countries). But at least it will stop the size of the Bundestag from growing out of proportion.