What is the purpose of a mediator when two parties disagree?
When two parties disagree, a mediator works to bring them to a meeting of the mind. The mediator helps each side give here and give here until they finally agree and sign a contract. This resolves the controversy by producing agreement between them.
Les explains that if two people have a controversy, you bring in a mediator. He points to labor unions and management, who cannot get together on a contract, so they bring in a mediator. The purpose is to make a meeting of the mind, to give here and give here, and then finally agree and sign a contract. He then contrasts this with God's covenant work: God is not going to use a three-person mediation. God is the mediator, the instigator, and the fulfiller, and He alone is involved. This fits the larger point that the covenant promise to Abraham was spiritual and heavenly in origin, and though Abraham's offspring broke it, God kept it settled and will finish and fulfill those covenant promises.