While there are country-specific factors for these declines, most social scientists agree that the root causes are structural. The share of center-left voters remains stable, but social democrats are increasingly unable to mobilize them. Silja Häusermann, a political scientist at the University of Zurich, argues that the cleavages parting European societies have shifted from the economic and class-related factors that dominated the postwar period toward issues like migration and climate change. Such issues divide culturally more liberal globalists from the culturally more conservative “communitarians” — both of which were once to be found among traditional social-democratic voters.

Add to that the loss of industrial labor as a social identity, the decline in union membership, and the rise of green parties, populist parties and parties on the extreme left that offer more tailored policies and identities — all of these challenge the former big-tent model of left-wing political organizing.

Under the pressure of decline, many of Europe’s social democratic parties have slipped into leadership brawls and harsh battles over their parties’ course. Too often, they grasp at faint hopes — marginal successes by, say, the Portuguese left, with its recipe for fiscal discipline and stimulating growth, or the Danish Social Democrats, who have leaned into anti-immigrant rhetoric.

Open primaries, which other parties in Europe are considering, can have a moderating effect if a party’s base is more moderate than its leadership, said Thomas Poguntke, a political scientist at the University of Düsseldorf. In Italy, he points out, Matteo Renzi managed to defend his centrist course within the Democratic Party in 2013 against leftist opposition among the leadership by relying on a primary that was open to nonmembers.

At the same time, open primaries can skew the results, allowing unorthodox candidates, like Donald Trump, to overcome establishment opposition. In France, the far-left candidate Benoît Hamon took control of the Socialist Party from the mainstream front-runner Manuel Valls. In Britain, the pacifist Socialist Jeremy Corbyn was elected leader of the Labour Party in 2015 in an election opened up to “registered supporters” who could join the vote for three pounds.

Among the German candidates, there is no Jeremy Corbyn; even those who advocate leaving the Grand Coalition are relatively moderate in their politics. Still, the stakes are still high, as are the risks. The SPD’s primary is fostering the illusion that a new leader, or a short-term move like leaving the government, will cure what ails the party. None of it grapples with the tectonic shift in European politics away from centrist compromise and toward hardheaded polarization.

The future of Europe’s Social Democrats will be decided less upon who leads them, and more upon whom they can attract to build a new, lasting base. It’s not about whose faces are on the poster. It’s what they have to offer. And so far, Europe’s social democrats haven’t figured that part out.