Gemara

(R. Avahu): When Chananyah went to Chutz la'Aretz to establish leap years and determine months, R. Yosi ben Kiper and the grandson of Zecharyah ben Kevutal were sent to protest.

Chananyah was Metamei, and R. Yosi and his colleague were Metaher. Chananyah forbade, and they permitted.

63b - Question: Granted, they could be Metamei what he was Metaher, for they are more stringent;

However, they could not be Metaher what he was Metamei, for this is a leniency!

(Beraisa): If a Chacham declares something to be Tamei or forbidden, another Chacham may not be Metaher or permit it.

Answer: There was a special need to undermine his authority, lest others be drawn after him.

Avodah Zarah 40a: A boat laden with Chilak came to Sichra. Rav Huna bar Chinena saw scales on the walls of the boat. He permitted the Chilak.

Rava: Perhaps some of the fish are Tamei!

Rava's announcers forbade, and Rav Huna bar Chinena's announcers permitted.

57b: A case occurred in Isur a Nochri stuck his hand in Reuven's wine and shook it. Reuven poured it into a barrel (with more wine).

Rava: (All) the wine may be sold to Nochrim.

Rav Huna bar Chinena and Rav Huna brei d'Rav Yehoshua: One may not benefit from it!

Rava's announcers permitted, and Rav Huna bar Chinena's announcers forbade.

Sanhedrin 33a (Mishnah #1): A monetary verdict can be overturned.

Contradiction (Mishnah #2): If a judge acquitted the guilty or obligated the innocent, or he declared Tamei what is Tahor or vice-versa, what he did stands. He must pay for the loss that he caused.

Answer #1 (Rav Yosef): Mishnah #1 refers to an expert judge. Mishnah #2 discusses an amateur.

Question (Mishnah): An expert is exempt (if he erred. If he can overturn his verdict, there is nothing to pay for!)

Answer #1 (Rav Nachman): A bigger Chacham can overturn the verdict. If there is no bigger Chacham, the verdict stands.

Answer #2 (Rav Sheshes): If he was To'eh bi'Dvar Mishnah (made a clear mistake), we overturn the verdict. If he was To'eh b'Shikul ha'Da'as (ruled unlike the primary opinion), the verdict stands.

Answer #2 (Rav Chisda): If the judge himself transferred the money, the verdict stands. If he did not, we overturn the verdict.

Rishonim

Rosh (Avodah Zarah 1:3): If Reuven asked a Chacham (Ploni) and he ruled that it is Tamei or forbidden, Reuven may not ask another Chacham (Almoni) so he will be Metaher or permit it. What is the reason? Perhaps Ploni erred, and Almoni will convince him to retract! The Ri says that the Gemara forbids asking Almoni Stam, so that (perhaps) he will permit it, and Reuven will rely on the Heter. Since Ploni already forbade it, to Reuven it is like a piece of Isur. Therefore, he may tell not rely on Almoni's Heter. However, he may tell Almoni 'I asked Ploni, and he forbade. What do you think?' If it seems to Almoni that Ploni erred, he can discuss it with Ploni. If he can prove to him that he erred bi'Dvar Mishnah, he retracts. If Almoni argues with Ploni about Shikul ha'Da'as, and he cannot prove from a Mishnah or Amora (that it is permitted), he says 'I say so, but I do not permit what you forbade, since you made it like a piece of Isur, and I cannot refute you from a Mishnah or Amora.' Below (40a and 57b), we find that one Chacham forbade, and another permitted. There, the question came in front of both of them (together) in the Beis Midrash. Or, the first opinion permitted. (Therefore, the second was allowed to disagree.) However, the Yerushalmi says that if a Chacham was Metaher or permitted, his colleague may not be Metamei or forbid. We must say that this is when the first Chacham's Heter already took effect before the latter disagreed. This is if he was not To'eh bi'Dvar Mishnah. If so, we must say that the question came in front of both of them in the Beis Midrash.

Question (Rashash 63b DH Ela): The Gemara connotes that R. Yosi ben Kiper and Zecharyah's grandson were in the Beis Midrash with Chananyah when questions were asked. According to the Rosh, they may disagree. What was the Gemara's question?

Note: The Rosh must hold that surely, some of the questions were about matters that Chananyah had already ruled about.

Ya'avetz (63b DH d'Lo): They disagreed to be lenient only when they had a tradition, or if it seemed that one may be lenient. Normally, even in such cases one may not argue with a Chacham in his place, even to be lenient. It was permitted only in order to undermine Chananyah's authority.

Ran (Avodah Zarah 1b DH ha'Nish'al): The Ra'avad says that the Isur to permit what another Chacham forbade is not due to the honor of the first. Rather, once the first forbade, he made it like a piece of Isur. Then, it cannot be permitted. Even if another permitted it, it is forbidden. In Chulin 44a, we say that the latter is not Reshai (permitted) to permit. I.e. even if he permitted, it is not permitted, even if he is greater in Chachmah and Minyan (number of Talmidim). The Gemara says that when there were two, we follow the greater Chacham. This is when they ruled together. This refers to when there is no argument about the matter; it is only Shikul ha'Da'as. If one erred bi'Dvar Mishnah, he can retract and be Metaher or permit, like it says in Bechoros (28b) and Sanhedrin. R. Tarfon ruled that a cow is Terefah. Had the cow been intact, he would have retracted, since he erred bi'Dvar Mishnah. We do not say so about Shikul ha'Da'as, because it became like a piece of Isur. The Rashba agreed.

Ran (ibid.): In Avodah Zarah (40a), it says that Rava's announcers forbade, and Rav Huna bar Chinena's announcers permitted. We must say that first Rav Huna's permitted, and then Rava's forbade. They could not permit after he forbade. Also the Ramban says so. This is difficult, for in Sanhedrin we say that if a Chacham erred b'Shikul ha'Da'as, we can retract his ruling! The Gemara concluded that both Mishnayos discuss To'eh b'Shikul ha'Da'as. We retract if he did not act himself to carry out his ruling. The Rif says so. If you say that monetary cases are different, i.e. one may reverse a ruling because it did not create a piece of Isur, why did Rav Chisda need to say that he cannot reverse it when he acted to carry it out? He could have said that one cannot reverse a ruling about Isur! Rather, one can reverse even Shikul ha'Da'as if the Chacham agrees. Another Chacham cannot reverse it without his consent, due to the honor of the first, and lest it seems that there are two Toros. Also, a bigger Chacham can reverse the ruling, even if the first does not consent. I say so l'Halachah, but in practice I cannot argue with the fathers of the world.

R. Yerucham (2:5, 22a): The Yerushalmi says that one cannot permit or forbid unlike the other, i.e. when they discussed the matter. Or, perhaps it discusses something that depends on reasoning. However, a bigger Chacham can overturn even something that depends on reasoning.

Poskim

Rema (YD 242:31): If a Chacham (Ploni) forbade something, his colleague (Almoni) cannot permit it through Shikul ha'Da'as.

Shach (53): The Ran citing the Ra'avad, and the Rivash (379), say that even a greater Chacham cannot permit. Divrei Chamudos (Chulin 3:24) says that it seems that the Rema holds like this. Maharik (171) holds that a colleague cannot permit, but a bigger Chacham can. The Ran (himself) and R. Yerucham say so.

Shach (54): The Ran citing the Ra'avad, and the Rivash (379), say that even b'Di'eved, if the latter permitted it is not permitted.

Rema (ibid.): Even if he erred b'Shikul ha'Da'as, he can discuss the case with Ploni until he retracts. Therefore, there is no Isur to ask a second Rav, as long as he tells him that Ploni forbade.

Gra (74): This is like it says in Sanhedrin. Even regarding Shikul ha'Da'as, we reverse the ruling, unless he acted to enforce the ruling. [The Ran] explains that he cannot reverse a ruling without the consent of the first Rav. Tosfos in Avodah Zarah (7a DH ha'Nish'al) says that he can reverse it when the Sugya favors the other opinion. Sanhedrin discusses such a case.

Rema (ibid.): Even if Ploni permitted and the Heter already took effect, Almoni cannot forbid through Shikul ha'Da'as. This refers to the same Hora'ah itself. Regarding another case, obviously Almoni can rule like it seems to him.

Shach (59): This is like the Rosh. Tosfos, Semag, and Hagahos Maimoniyos say that one can forbid even after the Heter took effect. They explain the Yerushalmi like this. Maharshal says so from Maharam, and it seems that the Ra'avad, Rashba and Ran agree, since they hold that the latter cannot reverse a ruling only because it became a piece of Isur.

R. Akiva Eiger: Todas Shelamim (Lachmei Todah 3 p.63) explains that if a Chacham forbade, another Chachamim cannot permit, even b'Di'eved, for it became a piece of Isur. If a Chacham permitted, we say only that another Chachamim should not permit, due to the honor of the first Chacham.

Gra (77): The Rema is like the Yerushalmi. This is difficult, for in Avodah Zarah one Chacham forbade, and one permitted! We must say that the first Chacham permitted. [The Rosh] answered that only if the Hora'ah took effect (another cannot forbid). When the first forbade [even before it took effect] another cannot permit, for it became a piece of Isur. Tosfos and the other Poskim say that one may forbid what another permitted. They explain the Yerushalmi oppositely. The Gemara in Berachos says like this explicitly.