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As for his daughter’s position, board members “put it in the paper, take resumes, and we wind up hiring who we think is best,” he said, noting that his daughter no longer works there.

But accountability depends on two things that don’t always happen: Union members being aware of the activities of their top officials, and the members acting on it.

Arthur Coia, for example, was president of the Laborers national — following in the footsteps of his father, who was treasurer — and was convicted of failing to pay taxes on a $1 million Ferrari. But even after the evidence became apparent, the union named him general president emeritus, with pay of more than a quarter-million dollars a year for life.

“They’re involved in everything from real estate to banking, and even if you had someone fall out of grace, there’s always a place for him,” Mr. Mehrens said.