Gemara

Monetary cases require three judges. A Mumcheh l'Rabim (expert judge) may judge by himself.

Sanhedrin 5a - Rav Nachman: Someone like me can judge monetary cases alone. (R. Chiya said the same.)

Question: Does he permit because he has learned and can reason, and he has permission (from the Reish Galusa - but without permission, his verdict is meaningless)?

Or, does it suffice that he learned and can reason?

Answer: A case occurred, and Mar Zutra brei d'Rav Nachman judged a case and erred. Rav Yosef told him that he is exempt only if the parties accepted him to be a judge.

This shows that even without permission, his verdict stands. (If not, there is nothing to be liable for!)

Rishonim

Rif (Sanhedrin 1a): Monetary cases require three judges. A Mumcheh l'Rabim may judge by himself. We learn from Mar Zutra that the verdict of a lone Mumcheh stands even if he did not have permission.

Rambam (Hilchos Sanhedrin 2:11): If one is Mumcheh l'Rabim or he received permission from Beis Din he may judge by himself, but he is not considered a Beis Din. Even though it is permitted, it is a Mitzvah mid'Rabanan to seat other judges with himself. Chachamim admonished 'do not judge alone', for there is only One lone Judge.

Rambam (5:18): Even though a Mumcheh may judge by himself, admission in front of him is not considered admission in Beis Din, even if he received Semichah. However, if there are three, even if they are Hedyotos, admission in front of them is a (proper) admission in Beis Din. If one denied money in front of them and was refuted by witnesses, he is Huchzak Kafran. The parties cannot change claims they made in front of them.

Lechem Mishneh: This is the Rambam's own reasoning. The Rosh disagrees.

Rosh (Sanhedrin 1:2): According to the opinion that Eruv Parashiyos does not apply here, a Mumcheh l'Rabim can judge alone. Mid'Oraisa, even a layman suffices. Chachamim enacted that three should judge. Regarding a Mumcheh, they leave the law like mid'Oraisa. Regarding a layman, l'Chatchilah he must judge amidst three. B'Di'eved, if he judged alone it is valid. According to the opinion that Eruv Parashiyos applies here, the Torah requires three Mumchim. Chachamim enacted that three laymen or one Mumcheh suffices. If one or two laymen judged, b'Di'eved it is invalid. Mumcheh l'Rabim means one who has learned and can reason. Rav Shrirah Gaon says that it is someone like Rav Nachman in his generation. He must be fluent in Mishnah, Gemara, Shikul ha'Da'as (the mainstream opinion in matters in which there was not a clear-cut ruling), has investigated Dinim for many years, and has been tested many times and has not erred. Such a judge can judge a person against his will. The parties can accept a judge even if he is not Mumcheh l'Rabim. We learn from this that three Hedyotos can judge a person against his will when he does not agree to come to Beis Din, for they are in place of a Mumcheh.

Beis Yosef (DH umi'Divrei): The Rosh connotes that a Mumcheh l'Rabim is like a Beis Din of Hedyotos in every respect.

Rosh (ibid.): Rashi says that the parties asked Mar Zutra to give them the proper Din Torah. If so, how do we infer that he must be learned and can reason? Even if he was not, his verdict would stand and he would be liable! (We establish the Mishnah 'If one judged...he must pay' to be when they accepted on themselves one who is not Mumcheh.) Rather, Mar Zutra judged them against their will. Since he was learned and could reason, his verdict stood even though he had not received Reshus.

Poskim

Shulchan Aruch (CM 3:2): If less than three people judged, the verdict is invalid unless the parties accepted them, or if the judge was Mumcheh l'Rabim.

Rema: Nowadays a Mumcheh l'Rabim cannot judge people against their will.

Prishah (6): Mahariyo says that nowadays there is not a Mumcheh l'Rabim who can judge people against their will. The Tur and Rosh do not distinguish Mumcheh from Mumcheh l'Rabim. However, the Rambam calls Mumcheh one who is merely learned; if he can also reason, he is Mumcheh l'Rabim.

SMA (6): Similarly, we say that nowadays there is no Mumcheh fitting to permit vows by himself (YD 228:1).

Shach (7): Nowadays Mumcheh l'Rabim does apply to exempt paying for mistakes, and that his verdict is binding.

Shulchan Aruch (ibid.): If they are less than three (Rema - and the parties did not accept them, and they are not Mumchim l'Rabim), even if they received Semichah in Eretz Yisrael, admission in front of them is (invalid) like admission outside of Beis Din. The parties can make claims (when they later go to Beis Din) unlike their claims in front of the first judges. If one denied money in front of them and was refuted by witnesses, he is not Huchzak Kafran (established to be a denier).

Question (SMA 7): The Rema connotes that if they are Mumchim, even if they are less than three, admission in front of them is considered admission in Beis Din. This is like the Tur and Rosh; it is unlike the Rambam. The Mechaber holds like the Rambam. He says 'even if they received Semichah, admission in front of them is not like admission in Beis Din', even though one with Semichah is presumably Mumcheh. The Rema should have explicitly said that he argues with the Mechaber!

Answer #1 (SMA 7). Perhaps the Rema calls Mumcheh l'Rabim someone whom the Tzibur accepted upon themselves. In this case, (the Mechaber agrees that) admission in front of him is valid.

Answer #2 (Shach 8): The Rema refers to a regular Mumcheh l'Rabim. He did not explicitly say that he argues with the Mechaber because it is not clear that the Mechaber disagrees; not everyone with Semichah is Mumcheh l'Rabim. The opinion of the Rambam and Mechaber is primary. Sefer ha'Terumos, Ir Shushan and Ba'al ha'Itur agree with it.

Answer #3 (Taz): The Rema explains according to the Rosh that admission in front of a Mumcheh l'Rabim is considered admission in Beis Din, but admission in front of a plain Mumcheh is not.

R. Akiva Eiger (DH v'Yecholim): One may change from what he claimed outside of Beis Din because people reveal their claims only in front of Beis Din. Regarding this, a Mumcheh is as good as a Beis Din (Maharit 2:CM:46). The Rambam says that admission in front of a Mumcheh is not like admission in Beis Din, i.e. it is not a document. The Rashba (Teshuvah 1126) says that if the parties accepted a lone judge, he is like a Beis Din regarding admission, Huchzak Kafran and changing claims. Keneses ha'Gedolah says that the same applies to a lone Mumcheh.

Shulchan Aruch (3:3): Even though a Mumcheh may judge by himself, it is a Mitzvah mid'Rabanan to seat other judges with himself.

Source: Avos 4:8

Taz (DH Af Al Pi): If the parties accepted him, he may judge alone l'Chatchilah. The Yerushalmi supports this. The Maharshal disagrees, but others refuted his proofs.

Aruch ha'Shulchan (5): If the parties accept one judge upon themselves, or he is Mumchim l'Rabim, he is like a Beis Din regarding admission, changing claims, and Huchzak Kafran, with only one difference. Admission in front of a Beis Din is like a document. If the first Beis Din accepted testimony, heard claims or ruled (and wrote this), another Beis Din can rely on it. It is not considered Ed mi'Pi Ed. Regarding a lone judge (who was accepted or Mumcheh l'Rabim), whatever he writes is like Ed mi'Pi Ed. He must testify in front of the latter Beis Din.