Stated another way, she must decide whether to rely on voters or on institutions.

Those are the two most fundamental building blocks of democracy. But in Germany, as in much of the rest of the West right now, both seem increasingly unreliable.

The result is that democracy now feels like a dangerous game. And even Ms. Merkel, arguably the Western leader who plays it best, has not figured out how to win.

Democracy … Except Some Votes Don’t Really Count

As the far right rises across Europe, mainstream parties, seeing an existential threat to liberal democracy, have searched for ways to contain its influence. The solution that major European powers like France and Germany have settled on — and that will be a component of any solution to Ms. Merkel’s current dilemma — is a so-called cordon sanitaire against the far right.

The term, which roughly translated means “quarantine” in French, means sealing off the far right from any power or influence, no matter how many votes it wins. Mainstream parties will not allow the far right into political coalitions or work with it on joint legislation. In Germany’s case, that means an absolute refusal to allow the far-right Alternative for Germany, or AfD, into any governing coalition. The party recently won seats in Germany’s national legislature for the first time.

In the short term, such policies have effectively limited the influence of both longstanding far-right parties like the National Front in France and insurgent upstarts like the AfD. To the many politicians and citizens who fear what might happen if the far right were to exercise real power, that feels like an important victory.