Can someone describe for me if this election system is a majoritarian system or a system of proportional representation? And how does it work?
It is an interesting mix of both called Mixed-Member Proportional Representation.
- Half the seats are regional representatives elected in a first-past-the-post system in each district ("Direktmandat").
- The other half is elected in a proportional representation system from lists decided by the parties themselves ("Listenmandat").
- But proportional representation is still guaranteed by a mechanism called "Überhangmandate" ("overhang seats") I will explain further below.
The voters have two votes in each federal election, one for the direct candidate in their district ("Erststimme") and one for the country-wide party list ("Zweitstimme"). So it is possible to vote someone from party A as your direct representative but vote for the list of party B ("vote splitting").
Those candidates who got the majority of candidate-votes in their district get a seat. This is exactly half of the nominal size of the Bundestag (299 / 598 seats).
The remaining 299 seats get divided among all parties which reached the election threshold (at least 5% list-votes or at least 3 direct representatives). The distribution is based on their relative number of list votes (using the D'Hondt method, if you want to know exactly). The party lists are ranked by the party. So if a party got enough list-votes for 50 list-seats, they get their top 50 candidates into the Bundestag, in addition to those they already got through direct representation.
The possibility of vote splitting and the spoiler-effect in in first-past-the-post elections means that the party distribution among direct representatives might not match the distribution of list-votes. So it is possible that parties now have a larger or smaller representation in the Bundestag than the fraction of voters who voted for their party list. To prevent this situation, those parties which are underrepresented gain additional seats from their party list ("Überhangmandat"), until the relative strengths of the parties matches their relative counts of list votes. That means the Bundestag can grow or shrink by a few seats each legislative period.
This system has several advantages over pure majoritarian district representation or pure proportional representation:
- You still get a regional representative from each district
- The relative strength of parties matches the popular vote (well, minus those votes for parties which didn't reach the election threshold)
- There is little incentive to do strategic redistricting ("gerrymandering"). The only reason for a party to shape voting districts is to improve the chance that a certain person gets their direct mandate. But if they want that person so badly, they can just give them a good rank on their party list.
But there is also a flaw in proportional representation this system does not fix: Those who manage to get a good position on a party-list of a major party are almost guaranteed to get a seat. The only way for voters to prevent such a person from getting elected would be to not vote for the party list at all, but that way they would also punish everyone on the list who comes after them.
The previous answer was mostly right, but I think it got a few crucial details wrong ...
The Bundestag has a default number of seats, currently 598 seats. There are 299 electoral districts, half that number.
- Individuals can run as Direktkandidat (direct candidate) in a district, either as a party candidate or as an independent candidate. The party members select the party candidate. An independent candidate or a candidate from a party which performed very poorly at the last election needs to gather supporting signatures to get onto the ballot.
- In addition, parties run with lists of candidates which are determined by the party membership prior to the election.
As explained by Philipp, the voters can then cast two votes, the Erststimme for the direct candidate and the Zweitstimme for a party.
- Direct candidates who get a plurality of the votes in their district are elected as direct representatives. There is no run-off election even if no candidate wins an outright majority. Direct representatives are half (or less) of the Bundestag.
- The remaining seats are distributed among candidates from the party lists (in the order of the list) so that the total percentage of representatives matches the Zweitstimmen percentages. However, only parties with three direct representatives or 5% of the Zweitstimmen will get any of the remaining seats. (As Martin reminded me, these lists are on a state level. This may lead to some rounding effects, but there are only 16 states in Germany.)
- Candidates can run both directly and on the list. If they become direct representatives, the next one on the list moves up for list purposes.
- If a direct or list representative resigns or dies during the term of office, the next one from the party list moves up. There are no special elections to fill that seat. If a representative decides to leave the party, he or she keeps the mandate and becomes an independent (or joins another party).
- It is possible that a party has more direct candidates in the Bundestag than their ratio of Zweitstimmen would indicate. In this case, the size of the Bundestag is increased and more list candidates from the other parties get in.
The last point shows that a high position on a party list does not guarantee a seat in the Bundestag -- a party with 30% or 40% of the vote might well win a plurality in most districts, so only direct candidates from this party come through. The first couple of list positions in a 10% party are almost sure to get in, however.
Philipp's other point about unpopular candidates high on the party list is right, and it is kind-of-intentional. The list mechanism allows parties to get e.g. their budget expert in even if he or she is no charismatic speaker.
Your question is a very good one as the system is complex and it's difficult to understand how the rules impact the composition of the parliament. The other answers do a decent job of describing some of the mechanics of the electoral system but they fail to provide a straightforward answer. It's typically described as a “mixed” system but that obscures more than enlightens and explains why many people are still confused about it even when they know quite a bit about the rules. The thing that got lost in the discussion is that the Bundestag effectively uses a proportional representation (PR) system. Quite simply, in practice, the composition of the Bundestag closely tracks the proportion of the Zweitstimme.
Consequently, the voting system used for the German Bundestag has none of the advantages of a truly majoritarian system (clear-cut results, simplicity…) and all those of a PR system. That's its most important feature and the reason why criticism based on actual or potential paradoxes do not hold much water. On the other hand, the first-past-the-post aspect adds a lot of complexity that explains why the two other answers got some small details wrong and failed to highlight the most salient feature.
But if you look at the political system, Germany only has a few large political parties represented in the federal parliament. That makes for simpler coalitions (compared to Italy, Israel, or the Netherlands for example) but is somewhat atypical for pure PR systems. That's by design and is mostly down to the 5% threshold to be awarded seats in the Bundestag. This rule didn't exist for the first two elections to the Bundestag and was introduced specifically to kill some small political parties. That's the second most important feature of the system.