Gemara

50b: Benei Baishan were stringent not to go from Tzur to Tzidon on Erev Shabbos. The next generation asked 'must we must follow this stringency? Our ancestors could be stringent. We cannot!'

(R. Yochanan): Since your ancestors accepted this, you must follow it - "Shema Beni Musar Avicha v'Al Titosh Toras Imecha."

Benei Chuzai used to separate Chalah from rice [bread].

(Rav Yosef): A Zar should eat rice 'Chalah' in front of them [to show that it is not Chalah].

Question (Abaye - Beraisa): If some people forbid certain things, you may not permit them to them.

Answer (Rav Yosef): Rav Chisda taught that this refers to Kusim

Question: One may not permit things to Kusim, lest they come to be lenient about other things. The same applies here!

(Rav Ashi): Rather, if most of the bread they eat is rice bread, a Zar should not eat rice 'Chalah' in front of them, lest they forget the law of Chalah;

If most of the bread they eat is not rice bread, a Zar should eat rice 'Chalah' in front of them, lest they separate Chalah from what is liable on behalf of what is exempt, or vice-versa.

(Beraisa): If some people forbid certain things, you may not permit them to them.

(Rav Chisda): This refers to Kusim.

Question (Beraisa): Two brothers may bathe together. In Kavul (a certain place), they do not;

Once, two sons of R. Gamliel, Hillel and Yehudah, bathed together there. The whole region was in an uproar.

Hillel [left the bath and] went to the outer room. He did not want to tell them that it is permitted.

Answer: Since Chachamim are scarcely found overseas, people there are [unlearned] like Kusim.

Nidah 20b: Yalta showed blood to Rabah bar bar Chanah. He was Metamei. She showed it to Rav Yitzchak brei d'Rav Yehudah, and he was Metaher.

Question (Beraisa): A Chacham may not be Metaher what another Chacham previously was Metamei.

Answer: Rav Yitzchak was Metamei until she told him that Rabah used to be Metaher that color, but this time his eyes were weak.

Inference: A woman is believed to say that a certain Chacham was Metaher this color!

Rejection: Rav Yitzchak had a tradition that the color is Tahor.

Chulin 44a: Rav was checking a Kaneh (windpipe) to see if the majority of the width was cut.

Question (Rav Kahana and Rav Asi): You taught that we require only the majority of the interior!

They sent it to Rabah bar bar Chanah to check. He checked for the majority of the interior. He was able to rule that it is Kosher, because Rav never ruled that it was Terefah. He bought some of the meat [for himself].

Question: It is improper to eat from an animal that a Chacham needed to permit!

Answer: This is if he permitted through reasoning. Rabah bar bar Chanah had a tradition that it depends on the majority of the interior.

49a: A needle was found in the great chamber of the liver. Huna Mar brei d'Rav Idi ruled that it is Terefah. Rav Ada bar Minyomi was Machshir.

Sanhedrin 33a (Mishnah #1): A monetary verdict can be overturned, whether Zechus or Chiyuv.

(Rav Yosef): This refers to an expert judge.

Question (Mishnah): An expert is exempt. (If he can overturn a mistaken 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 erred bi'Dvar Mishnah (a clear mistake), we overturn the verdict. If he erred b'Shikul ha'Da'as (ruled unlike the primary opinion), the verdict stands.

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. 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.

Rosh (Chulin 3:7): The Gemara said that Rabah bar bar Chanah was able to permit because Rav never forbade. It asked why he ate from an animal that required a ruling, and answered that he relied on his tradition. Now we do not need the first answer. Even if Rav had forbidden, Rabah could rely on his tradition to permit. A Chacham may not be Metaher or permit the same matter that another Chacham was Metamei or forbade, i.e. based on his own reasoning, but he may do so if his Rebbi taught him otherwise, like we say about the needle found in the liver. Also, hat Yitzchak brei d'Rav Yehudah was Metaher what Rabah bar bar Chanah was Metamei, because he had a tradition.

Hagahos Ashri: The Ri rejected the proof from the case of the needle. Both of them ruled together. He says that if the first permitted, afterwards another Chacham may forbid.

Tosfos (Avodah Zarah 7a DH ha'Nish'al): If Ploni forbade, why can't one ask all the Chachamim? They will discuss it, and perhaps they will convince Ploni to retract! I answer that it is forbidden only if the asker does not say that Ploni already forbade. Surely, the new Chacham may not permit, unless he can convince Ploni that he erred bi'Dvar Mishnah or Shikul ha'Da'as. If Ploni permitted, another Chacham may forbid. In Chulin 49a, Rav Ada permitted what Huna forbade because they were together at the time.

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. I disagree. 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. This is why Rabah bar bar Chanah permitted not in front of Rav. Also, a bigger Chacham can reverse a ruling, even if one who ruled first does not consent. I say so l'Halachah, but in practice I cannot argue with the fathers of the world. (The Ramban and Rashba agreed with the Ra'avad.)

R. Yerucham (2:5, 22a): If Ploni forbade, and it seems to Almoni that he erred, he discusses it with him. If he erred bi'Dvar Mishnah, he reverses it. If it depends on 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.' Some say that the latter cannot permit even if he has a tradition, unless it is a clear mistake. Others, including Rashi, say that a tradition to permit what the other forbade [helps even for Shikul ha'Da'as].

Poskim

Rema (YD 242:31): If a Chacham (Ploni) forbade something, his colleague (Almoni) cannot permit it through Shikul ha'Da'as. However, if he has a tradition that Ploni erred, or Ploni erred bi'Dvar Mishnah, he can permit.

Gra (72): In Nidah (20b DH Agmerei), Tosfos said like the Rosh, that once we say that he had a tradition, we retract from the previous answer. However, in Avodah Zarah (7a), Tosfos answered that both were asked together.

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.

Shach (55): Darchei Moshe brings so from R. Yerucham in the name of Rashi and others. However, Tosfos (Chulin 44b) and Hagahos Ashri citing Mahari'ach disagree. The Maharshal rules like them; it seems that this is primary. The Ran and Rashba agree.

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.

Taz (18): The Rema should have said 'if Ploni's Heter took effect...' Why did he say 'already'? It seems that they already relied on the Heter to be lenient, e.g. they ate some or it became mixed with Heter. Mere acceptance of the ruling does not prevent another from forbidding through Shikul ha'Da'as.

Shach (60): The Maharshal brings from the Mordechai that if the Chacham forbade for a stringency or a fence, another cannot permit even in another case.

Gra (78): We find in Eruvin 41a [that a later generation forbade what a previous generation permitted], and also in several places.

R. Akiva Eiger: In CM 25 (see below), the Shach retracted from what he wrote here.

Shulchan Aruch (CM 25:2): If one erred about Shikul ha'Da'as, and followed one opinion, and did not know that the entire world follows the other opinion, if he received permission [to judge] from the Reish Galusa, or the litigants accepted him on them, if he is an expert judge, the ruling is retracted.

Shach (14, Os 16): L'Halachah, Rav Sheshes' opinion is primary. One can retract (a ruling of Isur) only if in a parallel case regarding money, one could take back the money that he already paid to the other party based on the ruling. This is why the Rosh and R. Yerucham say that if the latter Chacham can show the first that he erred bi'Dvar Mishnah, he retracts. If he argues about Shikul ha'Da'as, he says 'I hold like this, but I cannot permit what you forbade, since you forbade, and made it a Chatichah d'Isura, and I cannot refute you from a Mishnah or Amora.

Shach (14, Os 18): In YD, why did the Rema rule like the Ran? The Ran himself said that he cannot argue in practice! Also, the Ran said this according to the Rif, who rules like Rav Chisda. We rule like Rav Sheshes! The Rema himself (Sa'if 3) says that some rule like Rav Sheshes.