Mark Carter, a labor lawyer, has done his homework.
In a powerful editorial in the West Virginia State Journal, Carter writes:
If you support a secret ballot election when voting in the congressional elections, you need not allow Congress to throw out the secret ballot election when it’s your turn to vote in the workplace. At the urging of organized labor, Congress is considering purposefully supplementing coercion into union elections by denying the secret ballot. Perhaps what congressmen really need to know is that the ultimate use of the employee’s secret ballot could be voting them out.
That is the essence of the argument — a secret ballot for me, but not for thee.