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If no one party is currently strong enough to achieve a majority in the parliament on its own, they engage in often torturous coalition talks after the election to form a government.
The leader is then chosen by the coalition that holds the majority in the Bundestag, as the lower house of parliament is known.
The German election system itself is extremely complex and combines a classic first-past-the-post system with proportional representation.
Each person casts two votes on a single ballot paper.
In the first vote, people elect their chosen candidate in their electoral district to the Bundestag and the winner takes up the district's seat.
In the second vote, people choose their preferred party from some 29 parties participating in the election by a complex system of proportional representation.
The system works as follows. In each of Germany's 16 states, parties draw up "state lists".
Parties are awarded a certain number of seats per state depending on the proportion of votes they receive.
When all the first and second votes have been counted, the number of direct candidates is subtracted from the number of seats won through the second vote and the remainder is awarded to politicians in the order they appear on the list.
So, if a party scores three "direct" seats through the first vote but is eligible for 10 seats through the second vote, the top seven names on the party's state list would be awarded Bundestag seats.
However, if a party obtains more direct seats through the first vote than its proportion of seats through the second vote would justify, it keeps these seats as so-called "overhang" seats.
For example, in 2005, the Christian Democrats were eligible for 28 seats in the state of Baden-Wuerttemberg via the second vote, but actually won 31 direct seats through the first vote, thereby gaining three "overhang seats."
As a result, the Bundestag often has more than its legal minimum of 598 seats.
This quirk of the system could be crucial this time around, as Merkel's centre-right bloc is expected to score as many as 20 of these "overhang" seats, compared to around four for her SPD rivals.
This lowers the percentage of votes Merkel needs for her preferred centre-right coalition to around 46-48 percent, rather than 50 percent, analysts say.
In addition, in order to make it harder for smaller and potentially extremist parties to enter the Bundestag, parties must achieve at least five percent of "second votes" nationally.
General elections are normally held in Germany every four years. They are always held on a Sunday.
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