Steve sent me this question. It’s an interesting one. The Chief Justice appoints the Reporter of Decisions–this power was delegated by a statute–but done without the consent of the entire Court.
I thought of this recent article that argues that the Article II appointments clause permits Congress to vest the appointments power in “the Courts,” not the Chief Justice. I suppose an Associate Justice could argue that the appointment by the Chief alone is ultra vires, unconstitutional, and the appointment was void. That would be fun.