Sometimes litigants identify for themselves people who would arrange a compromise between them, whether adjunct to beis din or not in beis din. This thing is proper, because each side will move to the credit of the one who chose him, and the compromise will be appropriate. But specifically to move in an honest direction; however far be it from him to cheat on the compromise! Just as they are careful not to pervert the judgment, so too they are careful not to pervert the compromise.
We saw something similar in se’if 1, where the halakhah was given that a court must first try to find a settlement, and only (se’if 2) if that fails, does the court engage in adjudicating the case.
I would conclude from this that we are placing peace ahead of justice; better a resolution that leaves both parties on more amicable terms than to give the property to its real possessor.