(Bloomberg)—The U.S. Supreme Court said it will try for a second time to decide whether 5 million government workers can refuse to pay union fees, accepting an Illinois case that could deal a major blow to the labor movement's finances and clout.

Revisiting an issue that deadlocked them in March 2016, the justices will consider overturning a 1977 ruling that lets public-sector unions in 22 states demand fees from workers who aren't members. Those so-called agency fees are designed to pay for union representation on such matters as pay negotiations.

Union critics say the mandatory fees violate the Constitution's First Amendment, forcing workers to support unions that don't share their priorities on matters of public importance. The court will hear an appeal from Mark Janus, an Illinois government employee challenging a state law that allows agency fees.

"Janus and millions of other public employees are effectively being required to support a government-appointed lobbyist," his lawyers at the National Right to Work Legal Defense Foundation argued in the appeal.

The 1977 ruling, known as Abood v. Detroit Board of Education, said agency fees were constitutional so long as workers didn't have to cover the cost of political or ideological activities.

Two years ago in a case involving California teachers, the court's conservative wing had appeared to be on the brink of overturning Abood. But Justice Antonin Scalia's February 2016 death left the group without a fifth vote, and the court instead split 4-4. Justice Neil Gorsuch's arrival on the court may mean the effort to topple Abood is back on track.

Union leaders say that collecting what they call "fair-share fees" ensures that workers can push for higher wages and better job conditions. If the fees weren't mandatory, workers could become free riders, benefiting from union representation without paying for it, according to a branch of the American Federation of State, County and Municipal Employees that represents Janus and other Illinois workers.

"Abood acknowledged that certain labor-relations interests justify the small intrusion on employees' First Amendment interests that fair-share payments represent," the union argued.

Janus works as a child-support specialist at the Illinois Department of Healthcare Services. He was one of three employees who took over a lawsuit originally filed by Illinois's Republican governor, Bruce Rauner.

A federal judge said Rauner didn't have the legal right to challenge the Illinois law, leaving the employees to press ahead with the case. A federal appeals court eventually ruled against Janus, saying Abood remained valid law.

Illinois Attorney General Lisa Madigan, a Democrat, is defending the state law alongside the union. Illinois is one of 22 states that permit agency fees, according to the National Right to Work Foundation.

The court will hear arguments early next year and rule by June. The case is Janus v. American Federation of State, County and Municipal Employees, Council 31, 16-1466.

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