Collaboration, however, is definitely not the only technique being used to successfully combat the perceived existential threat. Stuart Appelbaum, the president of the Retail, Wholesale and Department Store Union, has become something of an organized-labor star by employing the old-school approach of unifying workers in distrust of rapacious managers in new ways. And his successes have come in unlikely places: vulnerable, often immigrant workers in low-skill, itinerant jobs. He recently organized the workers at five New York City carwashes and at a poultry plant in Alabama, a state particularly allergic to unions. “We don’t argue to owners, ‘We’re doing this for your sake,’ ” he said. “We’re not going to be the ones who say, ‘We think you have to cut back on things to make your stockholders more profitable.’ ”

Unlike factory workers, Appelbaum’s members don’t have any incentive to cozy up to management. They work in what economists call the nontradable sector: jobs that can’t be moved easily to a low-wage country. Low-skill workers in nontradable jobs actually have one small but important organizing advantage. U.S. cars can be made in Mexico, after all, but they have to be washed here. As a result, unions are seeking growth in other nontradable fields, like carpentry, plumbing and transit drivers. The top prize is a group that comprises the single largest number of jobs that must be done on American soil: Walmart workers.

Unfortunately neither of these approaches — collaboration or defiance — has solved the fundamental challenges of organized labor. Union membership has been falling since 1954, when about 35 percent of the U.S. work force was organized. (When excluding comparatively successful public-sector unions, less than 7 percent of workers are now organized.) It’s also hard to find anyone with a convincing explanation of how membership could grow. Many recent union fights, in fact, have been waged over issues that seemed settled long ago, like the bulwark against anti-union right-to-work legislation in Rust Belt states. Even Appelbaum’s great successes are modest. One of his biggest accomplishments, a 17-week strike at a Mott’s applesauce plant, prevented a wage cut but brought few new benefits to workers.

In France and Germany, where union coverage is drastically higher and protections are stronger, there has been a steady erosion in the past few years. President François Hollande of France recently brokered a master contract with the three largest unions that will make it easier for companies to lower salaries or to lay off workers when business drops. Most of the labor scholars I spoke to — all broadly sympathetic to the union movement — said the decline of private-sector unions will continue. Gary Chaison, a labor-relations specialist at Clark University, in Massachusetts, was especially blunt. “There’s no way of really dealing with the global impact. There’s very little you can do.” Those machinist and autoworker jobs will grow ever more scarce, leaving workers to compete for lower-skill, lower-pay work. Subsequently, those nontradable service-sector jobs, like retail and washing cars and carpentry, will become overcrowded.

What will an America with no private-sector unions look like? For many on the left, this is a dystopian future of inevitable worker misery. For many on the right, it would mean more competitive companies and a healthier economy. One thing seems fairly clear, though: where there is no collective bargaining, there is only individual bargaining. And that means each worker, sitting down with a manager, making an argument for a job or a raise or against some form of bad treatment.