Hazrat Sha'bi (may Allah have mercy on him) says that if the disputing parties agree upon the statement of one person, then it is permissible for them to act upon his statement.

It is narrated from Hazrat Ibn Sirin that two people, while arguing, came to Hazrat Ubaidah. He asked them, "Do both of you accept me as your arbitrator and judge?" They replied, "Yes." Then he gave a decision between them.