Q: Can beis din issue a ruling based on a compromise?
A: Halachah favors compromise. Thus, at the outset of the litigation, beis din should offer the litigants the option of compromise. Moreover, it is recommended that the Dayanim avoid attempting to rule only according the letter of the law, due to doubts in Halachah and disputes that have accumulated over the generations. Furthermore, in cases where it is not possible to verify the truth, or where an oath is required, the Dayanim can force a compromise. Ideally, the compromise should not vary from the likely ruling more than a third (pesharah hakrovah ladin). For a compromise to be binding, the parties must make a kinyan sudar beforehand (C.M. 12:2, 5, 7, 20).
Regardless, almost all arbitration agreements signed when litigating in beis din nowadays explicitly authorize beis din to rule according to the letter of the law and/or based on a compromise.