But what happens when the issue is less clear and a judge has the appearance of a conflict, but no personal stake in the outcome of a dispute? The court is considering a case that asks whether the Constitution requires judges to step aside in that instance.

The justices met in private Friday to discuss a lawsuit over a coal contract in West Virginia in which a state Supreme Court justice rejected calls to step aside because the leader of one company in the case spent more than $3 million to help him get elected.

Justice Brent Benjamin twice was in the majority in 3-2 decisions overturning a $50 million jury verdict against Massey Energy Co. Don Blankenship, Massey's president, chairman and chief executive officer, was a key Benjamin backer. Two other state court justices recused themselves from the case the second time it was under consideration.

The losing party, Harman Mining Corp., says the appearance of bias by Benjamin is so strong that Harman's constitutional rights were violated. Former Solicitor General Theodore Olson is representing Harman.