Germans overwhelmingly support their current chancellor, Angela Merkel, in her bid for re-election. She polls in popularity at double that of her closest rival, Peer Steinbrück. So the federal elections on Sept. 22 in Germany are yawner, right?

Not necessarily.

Germany’s complex electoral system – one that political scientists admit that many Germans don’t fully understand – means that theoretically come Sunday, she could lose her post. It’s highly unlikely. But what is possible, and looking ever more likely, is that she will be forced to govern in a coalition with Mr. Steinbrück’s Social Democratic Party (SPD), even though her conservative Christian Democratic Union (CDU) has a 15-point advantage, according to most polls. Here are some of the reasons why.

Who is competing Sept. 22?

Unlike in the US, the German chancellor is not directly elected. Rather, it is the parties that compete.

There are nearly 40 participating in the Sept. 22 election, but they must receive five percent of the national vote to be able to enter into the Bundestag, or Germany’s lower house. This threshold was established to keep fringe groups out of politics, as happened during the Weimar Republic before World War II.

“Having no stable government with a strong majority that could pass legislation led to the further breakdown of the [Weimar] Republic,” says Jürgen Falter, a professor of political science at Mainz University.

That means that five parties are most likely to capture seats in the lower house. They are: Ms. Merkel’s CDU, with its sister Christian Social Union (CSU) of Bavaria, polling at about 40 percent; the SPD, the center-left party that has long competed with the CDU. They are polling at about 25 percent of votes; the market-friendly Free Democratic Party (FDP), with whom Merkel currently has a coalition but which is struggling to meet the 5 percent threshold this election; the Greens, a leftist party that is polling at about 10 percent; and the Left, which is polling at another 10 percent.

Two other parties are thought to have an outside chance at being seated. The Alternative for Germany party, a new euroskeptic party, is polling at about 3 percent, and the Pirate Party, an Internet-freedom group that saw a boost amid the backlash to the NSA spying program in Germany, has seen its numbers at around 4 percent.

So why isn’t it obvious that Merkel will win?

The CDU has a 15-point lead ahead of its nearest rival, and it is highly probable that Merkel will become chancellor of Germany for a third term.

But even if the CDU gets 40 percent of votes, it does not have an absolute majority. Thus, it needs to form a coalition to control a majority of seats. Merkel’s current partner, the FDP, is flailing; even if it meets the 5-percent threshold, another conservative coalition might not comprise a majority.

“The overwhelming majority of the German population wants to have Angela Merkel as chancellor again, but in Germany you don’t vote for a chancellor,” says Carsten Koschmieder, a political science researcher at Berlin’s Free University. “It is about which coalition is the strongest, not which party is the strongest.”

How does the process actually work?

Voters cast two votes on the ballot: One is for a leader to represent his or her district, which ensures every region in Germany is represented at the federal level. The second vote is to select a party. This is the decisive vote because it determines the relative strength of each party in the Bundestag, which then votes for a federal chancellor.

The process can get complicated when voters “split” their votes – choosing a leader in their district from one party, and choosing a different party for their second vote. Read more about “overhang mandates” at the Bundestag website.

After the results come in on Sunday, the parties will get to the business of building coalitions. To form one, they must agree to a “treaty,” or contract, by negotiating their future government’s platform. Once a working coalition is formed, the president of Germany nominates the chancellor and the Bundestag votes.

What is the most likely outcome then on Sunday?

Since Merkel risks not being able to maintain her current conservative coalition, it is very possible that Germany will have a “grand coalition” between the CDU and SPD. While the two differ ideologically, most notably on taxes and ways to ensure a minimum wage, they have governed together before, including during Merkel’s first term. Mr. Steinbrück has said that he’d not govern with the CDU in a coalition, but most political analysts say this is posturing ahead of the elections, and that the two would most likely find a political compromise.

Another mathematical possibility is a coalition between the CDU and the Greens. But many dismiss this scenario outright since the two parties differ so fundamentally on so many policies.

Mathematically, the Greens, the Left, and the SPD might also be able to form a coalition, but many in the SPD have long ruled out governance with the Left; they would lose a great deal of credibility if they did an about-turn.

What does the rise of the Alternative For Germany mean for this race?

While euroskeptic parties have gained ground in Europe, they have not found much space in Germany. But the new Alternative for Germany party, which wants weaker European states like Greece to leave the eurozone, has been rising in the polls.

They were polling at only 2 percent for most of the year until Merkel’s finance minister said in August that Greece would likely need another bailout. Their percentages rose to between 3 and 4 percent. That’s still under the 5 percent threshold, but they do appeal to conservatives, and thus could “steal” votes away from both the CDU and FDP. They are an unknown entity that could be a game-changer in the election.

“We have no experience in regard to this group,” says Mr. Falter. “We do not know if there is hidden potential that doesn’t express itself in public opinion polls.”

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