Gemara

6a (Beraisa): Pesharah (compromise) requires three judges, just like judgment. Once the Din finished, one may not suggest Pesharah.

R. Eliezer son of R. Yosi ha'Galili says, one may not compromise. If one does, he transgresses. If one praises one who compromises, he angers Hash-m - "u'Votze'a Berech Ni'etz Hash-m." Rather, the law pierces the mountain (we follow it, no matter what it is).

This was Moshe's approach. Aharon pursued Shalom, and made Shalom between people - "...b'Shalom uv'Mishor Holach..."

R. Yehoshua ben Korchah says, it is a Mitzvah to compromise - "Emes u'Mishpat Shalom Shiftu b'Sha'areichem";

Question: There cannot be Mishpat and Shalom!

Answer: The Mishpat that brings Shalom is compromise.

Similarly, "va'Yhi David Oseh Mishpat u'Tzedakah" - the Mishpat that has Tzedakah is compromise.

R. Shimon ben Menasiya says, if two people come for judgment, until you sense what the verdict will be, you may suggest compromise, but not once you sense what it will be. "Poter Mayim... v'Lifnei Hisgala ha'Riv Netosh" - before the verdict is known, you may abandon the dispute (and pursue Pesharah).

(Rav Yehudah): A verdict is 'Ploni, you are liable. Almoni, you are Zakai (you receive, or are exempt).'

(Rav): The Halachah follows R. Yehoshua (ben Korchah).

Question: Rav Huna was Rav's Talmid, and he would offer the parties Din (law) or compromise!

Answer: R. Yehoshua means that it is a Mitzvah to offer (Din or) compromise.

Question: This is like the first Tana!

Answer: R. Yehoshua says that it is a Mitzvah to suggest Pesharah. The first Tana says that this is optional.

Question: If so, the first Tana is like R. Shimon ben Menasiya!

Answer: The first Tana argues. He allows Pesharah even after you sense what the verdict will be, until the verdict.

32b (Beraisa): "Tzedek Tzedek Tirdof" - pursue Din and Pesharah.

Rishonim

Rif and Rosh (1:4): The Halachah follows R. Yehoshua, i.e. it is a Mitzvah to offer Din or Pesharah. This is before the verdict. Once there is a verdict, one may not suggest Pesharah. A verdict is 'Ploni, you are liable. Almoni, you are Zakai. R. Shimon ben Menasiya says that once you sense what the verdict will be, you may not suggest Pesharah. The Halachah is not like him.

Shiltei ha'Giborim (1b:1, brought in Shach CM 12:6): The Isur to suggest Pesharah after you sense what the verdict will be, is only if the judges impose it without informing the parties. If they explain the Pesharah and persuade them to pardon each other or for one to give something to the other, this is permitted even after the verdict, as long as they only appease and do not force. This is a great Mitzvah of bringing Shalom between people.

Hagahos Ashri, citing Rashba: Rashi says that a verdict is 'Ploni, you are liable...' Or Zaru'a says that it is when the judgment is finished, and all that remains to do is say 'Ploni, you are liable. Almoni, you are Zakai.' Then, you may not compromise. However, if the claimant or defendant must swear, even if all that remains to do is say 'Ploni, you are liable...', you may suggest Pesharah, to avoid the punishment for an oath.

Bach (CM 12:3 DH u'Mah): Tosfos permits suggesting Pesharah to avoid an oath after the verdict, i.e. (according to Tosfos) once the judges sense what the verdict will be (but not after the verdict was given).

Rambam (Hilchos Sanhedrin 22:4): It is a Mitzvah to tell the parties at the beginning 'do you want Din, or Pesharah?' If they want Pesharah, we compromise for them. A Beis Din that always does Pesharah is praiseworthy. This is before the verdict, even if you heard their words and know which way the verdict leans. Once the case finished, and he said 'Ploni, you are liable. Almoni, you are Zakai', you may not Pesharah. The Din pierces the mountain.

Rosh (85:5, cited in Beis Yosef CM 12 DH Kasuv): A case occurred in which three made a Pesharah between a widow and her orphaned son. Her son did not have an overseer to claim for him. This was improper. Anyone may act to help orphans, but the mediators did not intend to be Apotropsim for him. If the Apotropos of the minor (who was appointed afterwards) finds that they erred, the mediatiors must retract. Even if they intended to be Apotropsim for him, they cannot appoint themselves to be Apotropsim. Only judges of the city, or Gedolei ha'Dor, who are the father of orphans, can appoint themselves or others to be Apotropsim. Three Stam people cannot. A Beis Din heard the Apotropos' claim, and ruled about it without Pesharah. I (the Rosh) cannot change this. One Beis Din does not look to change the ruling of another Beis Din (Bava Basra 138b)! The Apotropos says that the verdict is void because the parties did not select the judges. This is nonsense. Once the parties claimed in front of the Beis Din, they accepted them! However, if the ruling is unclear, or if there are new claims that were not made in front of the judges, you can send them to me.

Tosfos (6b DH Aval): Aharon was able to suggest Pesharah (after the verdict), for the Din came in front of Moshe, and not in front of Aharon.

Poskim

Shulchan Aruch (CM 12:2): It is a Mitzvah to tell the parties at the beginning 'do you want Din, or Pesharah?' If they want Pesharah, we compromise for them.

Beis Yosef (DH u'Mitzvah): Rashi and the Rambam hold that even if he first mentions Din, since he immediately offers Pesharah, this is called beginning with Pesharah. The Tur says that one must mention Pesharah first. However, the Gemara discusses mentioning Din first! He must hold that Rashi explains that even though the Gemara first mentioned Din, really one must mention Pesharah first, for it is the Mitzvah. Alternatively, the Tur holds that one may start with either.

SMA (6): Since the Mitzvah is Pesharah, we explain to the parties that Pesharah is better for them.

Shulchan Aruch (ibid): Just like Beis Din is commanded not to tilt Din, they are commanded not to tilt Pesharah to favor one side over the other. A Beis Din that always does Pesharah is praiseworthy.

Beis Yosef (DH uch'Shem): Rashi (32b DH Aval) explains "Tzedek Tzedek Tirdof" to teach that both Din and Pesharah must be like you see is proper, without pursuing one side more than the other.

Shulchan Aruch (ibid): Before the verdict, even if you heard their words and know which way the verdict leans, it is a Mitzvah to compromise. After the case finished, and he said 'Ploni, you are liable. Almoni, you are Zakai', you may not compromise between them.

Beis Yosef (DH u'Mah): Tosfos says that once the judges studied the case enough and they only need to say 'Ploni, you are liable', they may not trick Almoni into Pesharah. If he would know that it has been clarified that he is Zakai, he would never agree to Pesharah.' Rashi explains that they already said 'Ploni, you are liable...' The words of the Gemara support this, but it is difficult. What Pesharah can follow after the Din was given?! A weak answer is that they could trick him and say 'we fear lest we erred.' The Rambam and Tur hold like Rashi. This is primary.

SMA (9): Even if you see that the Din favors Ploni, it is proper to suggest Pesharah. It is better for him to give a little to his opponent in order that there will be Shalom between them.

Shach (4): The Bach says that one should be stringent like Tosfos (not to suggest Pesharah once you whom the Din favors). This is wrong, for Pesharah is the Mitzvah. Most Poskim say so.

Shulchan Aruch (ibid): Someone else who is not a judge may Pesharah between them, but not in a place where Beis Din is fixed to judge.

Beis Yosef (DH Motzasi): The Agudah permits one who is not a judge to compromise between them afterwards. The Rashba says in the name of Rav Hai Gaon that if the party obligated to pay went to (Nochri) authorities to avoid paying, others make a Pesharah not in a place where Beis Din is fixed to judge.

SMA (11): What is done in front of Beis Din is as if it was done with the judge's will and consent.

Shulchan Aruch (ibid): If Beis Din obligated one of them to swear, Beis Din may Pesharah between them to avoid the punishment for an oath.