The U.S. Supreme Court likely ignited an intense battle in state and federal courts with its decision Tuesday that class arbitration may not be imposed on parties who have not agreed to it.

“The sword of Damocles is hanging over class arbitration now,” said F. Paul Bland of Public Justice, a Washington-based public interest law firm. “I think you are about to see a huge battle begin for what the implications of the case are. Consumer and employee advocates are going to take a view very, very different from what you’re going to see from the defense bar.”