The activist Florence Reece wrote the union ballad “Which Side Are You On?” in the midst of Kentucky’s so-called Harlan County War in the 1930s.

Posed this question late last week by the United Auto Workers, employees of Volkswagen’s Chattanooga, Tenn., plant answered that they don’t want to be on the side of a union that is slipping into irrelevance. Once a 1.5 million-member behemoth, the UAW has seen its membership decline to a fourth of what it was in the late 1970s.

Everything had lined up for the UAW in Chattanooga. Not only was VW officially neutral, it tilted the playing field in favor of the union. The company allowed it to campaign in the plant — a major advantage — while opponents were excluded. The media was praising Volkswagen’s enlightened European attitude toward organized labor and celebrating imminent victory for the union.

Then the workers had their say. The UAW reportedly spent $5 million in the course of a campaign that lasted two years, and lost by a 712 to 636 vote.

The motto of the old American Federation of Labor was “a fair day’s wage for a fair day’s work.” VW workers felt they already had it. Wages in Chattanooga are comparable to those of new hires of the Detroit automakers, roughly $20 an hour.

The unionization of the workforce would make it possible for VW to form a European-style “works council” of management and workers to make decisions about the plant. But workers already felt amply consulted by management. Even UAW Secretary-Treasurer Dennis Williams attested, “Volkswagen’s a class act.”

This is hardly the “Battle of the Overpass,” when company thugs beat UAW officials trying to organize Ford in the 1930s. This is a car company putting out a welcome mat for union organizers who still couldn’t manage to organize.

Florence Reece wrote, “Come all of you good workers/ Good news to you I’ll tell/ Of how the good old union/ Has come in here to dwell.” But the workers in Chattanooga didn’t consider it such good news.

Bob King, the head of the UAW, thinks they’re guilty of false consciousness. If only they weren’t so viciously misled by outside agitators, like Tennessee Sen. Bob Corker, the former mayor of Chattanooga who helped to woo VW to the city in the first place. He rightly said that the UAW is in a “death spiral,” and more controversially, that the automaker would make a rapid decision to invest further in the plant if the UAW lost the vote.

King alleges that Corker’s comments violated “the spirit” of labor law, which is nonsense. The senator doesn’t work for VW, and he has the First Amendment right to say whatever he wants. If Corker is guilty of dirty pool, what about President Obama, who told a group of Democratic lawmakers that no one opposed the UAW organizing the Chattanooga plant except people “more concerned about German shareholders than American workers”? That’s not inflammatory.

The only law that will satisfy King is one that forbids anyone from saying a discouraging word about his union, which was found alone in a room in 2009 with two nearly dead car companies. After the UAW did so much to chase automaking out of Detroit with unsustainable labor costs and ridiculous work rules, it’s no wonder that workforces haven’t welcomed it into the South, where right-to-work states have become alluring destinations for foreign car companies.

For the longest time, the business model of the UAW has been to take its members’ dues and funnel them to friendly Democratic politicians. Unless it breaks into the South, the union knows it’s all but doomed. It may feel this institutional imperative keenly, but workers in good manufacturing jobs who owe nothing to this self-serving dinosaur from the 20th century don’t. They can be forgiven for wondering which side the union is on.