What they want is a law requiring employers to recognize unions just on the basis of signed cards, rather than a secret-ballot election, as explained in this American Spectator article.
As I have often said before, neither “card check” nor election procedures are appropriate. If a worker wants union representation, let him sign up with a union to see if it can deliver anything of benefit. No one who doesn’t want a union should be compelled by law to accept one. The problem is that the neutral rules of the common law of contract have been supplanted by the authoritarian rules of the National Labor Relations Act.
