That looks harder now — four parties have become seven, and the two larger parties shrunk — though not everyone thinks that is a bad thing.
Some analysts say it will bring more voices into the public debate, with the potential to revitalize politics. But it will no doubt make governing harder, as Germany becomes more like other countries in Europe — among them, Spain, Italy and the Netherlands — that have seen a similar political fracturing.
Wolfgang Merkel, director of the democracy and democratization unit of the Berlin Social Science Center, said the dwindling of consensus was a sign of maturity.
“The past 30 years we have experienced a disenchantment with politics that can be seen in the persistent drop in voter turnout since the 1970s,” said Mr. Merkel, who is not related to the chancellor. “Now, the important questions are being debated once again. You can say it is a revival of pluralism, of pluralist discourse.”
Ms. Merkel has embodied that tradition of consensus more than perhaps any of her predecessors. Of her three terms over 12 years, she has spent two in a grand coalition with her party’s traditional opponents, the Social Democrats. She has been a creature of a political center she has made ever more capacious.
Pragmatic, reactive, a scientist by training, Ms. Merkel rarely stooped to ordinary politics. She was instead Germany’s first post-ideological chancellor.
But politics and ideology have now come roaring back.
The Sept. 24 election returned a difficult result, with seven parties crowding into Parliament, including far-left and — for the first time since World War II — far-right populists.
That result not only reflected the country’s increasing fragmentation and polarization, but also a feeling among many Germans that the centrist dominance of Ms. Merkel had stifled political opposition and healthy debate.
More than a fifth of voters cast their ballots either for the nationalist Alternative for Germany, or for the post-communist Left Party. Both parties rode a wave of public discontent over migration and globalization.
“We want to go in a different direction from all the others, that is our purpose,” Beatrix von Storch, a deputy leader of the Alternative for Germany, or AfD, told the public broadcaster RBB on Monday, after the German president had urged parties to reconsider their positions.
“Our task right now is to bring about political change in this country. All parties are going in the same direction,” Ms. von Storch said. “They can happily join a coalition,” she added, “because there are hardly any differences between them.”
The coalition the chancellor had sought would have been the culmination of Merkellian consensus-building, spanning the mainstream political spectrum.
A straddle in the extreme, it aimed to join at one end the ecologist Greens — born out of an antinuclear pacifist protest movement — with the business-friendly Free Democrats at the other.
Ms. Merkel’s Christian Democrats and their Bavarian sister party, the socially conservative Christian Social Union, were to be the glue in between.
But instead of emphasizing points of agreement, party leaders appeared at pains to emphasize their differences, fearful of having their independent political identities subsumed.
The discussion at times notably veered from the collegial.
Three weeks into the exploratory coalition talks, the leading negotiator for the Christian Social Union, Alexander Dobrindt, declared that closing the country’s coal plants, a campaign promise of the Greens, would be “absolutely absurd.”
The Greens’ negotiator on climate issues, Annalena Baerbock, told the Berlin daily Die Tageszeitung that as they passed one another in the hallways during the talks, he had muttered in her direction, “Yes, yes, the Greens live in their beautiful, idyllic world.”
But it was not the split between the conservatives and the Greens that brought down the talks. It was a surprise move by the Free Democrats, whose party chief, Christian Lindner, walked out shortly before midnight on Sunday, citing irreconcilable differences.
“We are unwilling and unable to take responsibility for the spirit of the negotiation results,” Mr. Lindner announced. “We would be forced to abandon convictions we have spent years fighting for.”
A deal may still happen. President Frank-Walter Steinmeier began holding talks this week with all party leaders, hoping to find a solution. On Thursday, he met for more than an hour with Martin Schulz, leader of the Social Democrats, who had repeatedly ruled out another grand coalition, but has now agreed to meet with Ms. Merkel next week.
But even if the parties do agree to another grand coalition, that might not forestall the dawn of a messier, perhaps nastier, politics. It would leave the far-right AfD, the third-largest vote-getter in the election, as the country’s chief opposition party — something the political establishment had made clear that it wanted to avoid.
In its debut in the new Parliament, the AfD immediately signaled that it was not playing by the old rules of consensus. On the contrary, it proudly touted that it would not compromise.
The big dilemma of politics in the age of populists, said Yascha Mounk, a lecturer at Harvard University, is that “You either need to share government with people whom you are ideologically opposed to or you have no majority government.”
“There are no good solutions,” he said.
Another grand coalition would almost certainly cost the centrist parties even more ground and “allow the populists to rise further,” he said.
The centrist consensus of recent years has come at a price — even at a time of low unemployment, solid exports and a budget surplus of around 20 billion euros, about $24 billion.
“Those who are unhappy with the government are unhappy with both main parties and go to the extremes — that has happened,” said Professor Garton Ash. One of Ms. Merkel’s stock phrases, he pointed out, was describing policies as being “without alternative.”
“It may be no surprise that the populists call themselves Alternative for Germany,” he said.
Some said the return of vibrant debate was exactly what was needed.
Mathias Döpfner, chairman of the board of directors at the publisher Axel Springer, called on Germans to view a new political climate as an opportunity.
“The country must again get used to the idea that politics can be something other than just maneuvering,” Mr. Döpfner wrote in an editorial in the mass-circulation Bild newspaper on Tuesday. “A compromise is not always wise, but sometimes simply lazy.”
What some are viewing as a lack of stability in Germany, Mr. Merkel of the Berlin Social Science Center argued, was simply a correction of the system, aligning it with its other European partners.
Where two parties used to suffice, now three or even four are required. The Netherlands, Sweden and Spain have all had minority governments.
The challenge facing mainstream parties, said Professor Garton Ash, who wrote about the subject in The New York Review of Books, was to win back voters from the AfD without legitimizing its nativist rhetoric.
In one session, Mr. Lindner had insisted that he wanted those who had voted for the AfD to be able to vote for him, a shocked Green politician recounted.
“The question is: Can they do that without actually encouraging people to go to the far right?,” Professor Garton Ash said. “That is a challenge that is coming up fast.”
In recent years, Ms. Merkel has become almost synonymous with German leadership. Now, her inability to forge consensus risks becoming synonymous with a fractured, weakened Germany.
While Ms. Merkel is weakened, with no clear successor in the wings she also remains the strongest leader by default. “This is the beginning of the end of Merkel,” Professor Garton Ash said. “But it could be a very long end.”
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