How the election works
In elections to the Bundestag, or federal parliament, German voters cast two votes. The “first vote” is to elect a “direct” representative for their local constituency, much like in a British election: the candidate with the most votes wins the seat, except in some rare cases.
The “second vote” is for a party list, as in many European countries. The refinement of the German system is that the overall membership of the Bundestag is designed to be proportional to the second vote.
There are two last details that affect the assignment of seats. The first is that a party needs to cross a 5% threshold in the second vote to get party list seats. So in reality, the seats are awarded proportionally to the parties that do cross the threshold, based on their share of “successful” second votes. The other detail is that a party that wins three or more seats in the first vote, or which represents one of a small number of recognised minority ethnic groups, does not have to meet the 5% threshold.
Once the calculations are complete, the parties typically spend a number of weeks in coalition negotiations. Only when these are complete does the Bundestag vote to elect the chancellor.
