Gemara

83a - Mishnah: We are Mechalel Shabbos for any Safek Piku'ach Nefesh. If a house caved in, we unearth it (even if we must Mechalel Shabbos), even if we are unsure whether or not someone is there, and whether or not he is already dead, and whether he is a Yisrael or a Nochri.

84b - Shmuel: (There was a group of people and on Shabbos a house collapsed on one of them; we do not know who it is.) We do not follow the majority regarding Piku'ach Nefesh.

Question: What is the case?

If the majority are Yisrael, even if we would follow the majority we would unearth him!

Even if half were Nochrim, we would unearth for an even Safek!

Answer: There is one Yisrael and nine Nochrim.

Question: We never follow such a majority! The Yisrael is considered 'Kavu'a', i.e. it is considered like an even Safek.

Answer: The case is, they (Rashi - all) went to another Chatzer. (The Yisrael is not considered Kavu'a there.) One might have thought that we say that the one who separated (and entered the house) was from the majority. Rav Yosef teaches that this is not so. Regarding mortal danger we do not follow the majority.

Question: R. Yochanan taught that if there were one Yisrael and nine Nochrim (and a house collapsed on one of them), if it was in the original Chatzer we unearth, but in another Chatzer we do not!

Answer: We distinguish when only some of them went to the other Chatzer (Rashi - the Yisrael was not Muchzak there, for perhaps he did not go) from when all of them went to the other Chatzer.

Question: Elsewhere, Shmuel follows the majority regarding Piku'ach Nefesh!

Mishnah: When a baby is found, we assume that he is like the majority of the city. If half the city are Yisraelim, he is a Yisrael.

Rav: We follow the majority to support him, but not for lineage (for marriage).

Shmuel: (We follow the majority) to unearth him.

Answer: No, Shmuel comments on the Reisha of the Mishnah:

Reisha: If the majority are Nochrim, the child is a Nochri;

Shmuel: This does not apply to unearthing him (even if the majority are Nochrim, he is like a Safek Yisrael and we unearth him).

Question: According to Shmuel, regarding what does the Mishnah say 'if most are Nochrim, he is a Nochri'?

Answer (Rav Papa): We may feed him Neveilos.

Rishonim

The Rif and Rosh (8:15) bring Shmuel's teaching and the answers defending it. In their text, we answer the question of Kavu'a by saying that one of them went to another Chatzer. Therefore, the Rif (according to the Ran) and Rosh explain the answer to the contradiction with R. Yochanan as follows. If all of them left the original Chatzer, and while going one of them separated, we do not unearth. Since all of them left, the Yisrael is not Kavu'a. If only one separated, since the rest remained Kevu'im, it is considered an even doubt because of the severity of Piku'ach Nefesh.

Ran: This is like Shmuel. The Rambam rules like Rav and R. Yochanan, who follow the majority regarding Piku'ach Nefesh.

Rambam (Hilchos Shabbos 2:20): If there was even one Yisrael in a Chatzer with 1000 Nochrim and a house collapsed on them, we unearth because of the Yisrael. If one of them went to another Chatzer and a house collapsed on him we unearth, because perhaps it was the Yisrael.

Question: This is not a Chidush of Piku'ach Nefesh! The same applies if nine stores sell Kosher meat and one sells Neveilos. If one is unsure from which store he bought, it is considered an even Safek.

Answer (Magid Mishnah): Here is different, because when they separated there was no need to know which is the Yisrael. Our Safek arose (when the house caved in) after separation. This is like meat found in the street, which normally is not considered Kavu'a. Shmuel considers it like Kavu'a regarding Piku'ach Nefesh.

Rambam (ibid. 21): If all of them went to another Chatzer, and while going one of them separated and entered a different Chatzer and a house collapsed on him we do not unearth. Since all of them left there is not a Yisrael Kavu'a here. We say that the one who separated while they were going was from the majority. However, if the majority were Yisraelim, even if all of them went to another Chatzer and one separated to a different Chatzer and a house collapsed on him, we unearth him.

Ra'avad: Some explain that when all left we unearth because a Yisrael was Muchzak in the new Chatzer, but if only a few left we do not unearth because a Yisrael was not Muchzak there.

Question (Ramah): The Rambam explained in a Teshuvah that the Halachah follows R. Yochanan against Shmuel. The Gemara resolved that they do not argue. One discusses when all of them separate, the other discusses when only some separated!

Answer (brought in Kesef Mishneh): According to the Rambam, when the Gemara says that Shmuel comments on the Reisha this is a retraction. Shmuel does not follow the majority in Piku'ach Nefesh whether some or all separated. R. Yochanan follows the majority whenever it is not Kavu'a, like all Isurim. Some texts explicitly say 'Ela' (indicating a retraction).

Poskim

Shulchan Aruch (OC 329:2): We do not follow the majority regarding Piku'ach Nefesh. Even if there were nine Nochrim and one Yisrael in a Chatzer and one of them went to another Chatzer and a house collapsed on him we unearth him. Since the first Kevi'us remained in its place, it is considered an even Safek.

Source (Tosfos DH u'Lefake'ach): "V'aChai Bahem" teaches that we do not guard Mitzvos (with certain exceptions) if there is any chance that it will cause a Yisrael to die.

Question (Sha'ar ha'Tziyon 6): If so, we should unearth in every case, even if everyone separated!

Magen Avraham (2): Regarding other Isurim we follow the majority.

Mishnah Berurah (4): Even if the majority separated, as long as one of them remained the Kevi'us remains and it is like an even Safek.

Shulchan Aruch (ibid.): However, if all of them left, and while going one of them separated and entered a different Chatzer and a house collapsed on him we do not unearth. Since the first Kevi'us was uprooted from its place, we say that the one who separated was from the majority.

Magen Avraham (3): This is only if they left one by one. If all left together, they are still Kevu'im.

Shulchan Aruch (EH 4:34): If a child was found in the street and he was not Tovel for conversion, if half the city is Nochrim we do not Mechalel Shabbos to save him.

Beis Shmuel (58): Tosfos (Kesuvos 15a DH Dilma) says that it is not considered a Safek Kavu'a because the child was not found in his house. The Rambam says that it is because they move.

Rema: Some say that even if the city is mostly Nochrim we Mechalel Shabbos to save him.

Gra (DH v'Yesh Omrim): This is the preferred opinion.

Mishnah Berurah (329:6): If a baby was found on a road and most of the traffic is Nochrim, all agree that we follow the majority.