There was no moderator of the Lincoln-Douglas debates. There was a timekeeper, usually some respected town elder in Alton, Freeport or Galesburg, Ill., who would keep track of how long a candidate could speak, then say something like, "Thank you, Mr. Lincoln. Your turn now, Sen. Douglas," and vice versa.
But there was no moderator. Each candidate spoke in turn. They asked each other questions directly. They could accuse each other of being wrong, or not telling the truth, face to face, and did.