Gemara

(Mishnah): Coins found between the Shofar [box] with Shekalim [for Korbanos Tzibur] and Nedavah (for Olos), if they are closer to Shekalim, we put them with the Shekalim. If they are closer to Nedavah, or they are in the middle, they go to Nedavah.

Bava Basra 23b (Mishnah): A chick found between two dovecotes goes to the owner of the closer one;

If it is exactly in the middle, they divide it.

(R. Chanina): When in doubt about where something came from, we assume that it came from the majority, even if the minority is closer.

Even though the Torah says that we follow the majority, and that we attribute to the closest source, the majority is stronger.

Question (R. Zeira): "Ha'Ir ha'Kerovah" - we attribute (an unknown murderer) to the closest city, even though other cities have more people!

Answer: No, this is only when the populations are equal.

Question: If so, we should assume that the murderer came from the rest of the world!

Answer: We discuss an area surrounded by mountains.

24a (Rav): If a barrel (of wine) floating in a river was found near a city that is mostly Yisraelim, it is permitted. If the nearest city is mostly Nochrim, it is forbidden;

(Shmuel): Even if it was near a city of Yisraelim, it is forbidden. Perhaps it came from Ihi Dekira (a Nochri city upstream in Bavel).

Suggestion: Shmuel follows the majority like R. Chanina, and Rav argues and assumes that it came from the closest.

Rejection No, all agree with R. Chanina;

Rav holds that it could not have come from Ihi Dekira, for it would have broken on rocks in the river;

Shmuel holds that perhaps it floated in the middle of the river, where there are no rocks.

A barrel of wine was found in an orchard of Orlah. Ravina permitted it. (Most fruit in the world is not Orlah.)

Suggestion: Ravina holds like R. Chanina.

Rejection: No. He permitted only here, for a thief would not hide wine in the place he stole the grapes [lest they see him stomp them].

However, he would hide the grapes there.

Bava Metzi'a 24b (Rav Asi): If one finds a barrel of wine in a city that is mostly Nochrim, he may keep it, but he may not benefit from it;

If a Yisrael gives a Siman, the finder (keeps it and) may drink it.

Question: Since one may not benefit from it, why bother saying that he may keep it?

Answer (Rav Ashi): He may use the Kli that it was in.

Kesuvos 15a (Beraisa): If nine stores sell Kosher meat and one sells Neveilah and one does not know from which store he bought, the meat is forbidden.

If meat is found (in the market), we follow the majority.

Rishonim

Rosh (Bava Basra 2:22): Rav and Shmuel argue about a barrel found near a city that is mostly Yisraelim. We conclude that all agree with R. Chanina. They argue about whether or not we are concerned lest it came from Ihi Dekira, and floated in the middle of the river, where there are no rocks. The Halachah follows Rav in Isurim. If it is found near a city that is mostly Yisraelim it is permitted even if it is found near a Nochri's house, for we follow the majority of the city. A barrel of wine was found in an orchard of Orlah. Ravina permitted it, for we follow the majority, even against Kurva d'Muchach. Really, he would have permitted even grapes. We do not follow the majority of the world to forbid due to Yayin Nesech because most thieves are Yisre'elim, like it says in Avodah Zarah (70a).

Hagahos Ashri: We do not follow only Kurva, rather, the majority, so even grapes are permitted. At the least it is Safek Orlah, which is permitted in Chutz la'Aretz. One may benefit from wine, but not drink it nowadays that most thieves are Nochrim. In their days most thieves were Yisre'elim, so it was permitted even to drink the wine.

Nimukei Yosef (Bava Metzi'a Sof 13a): The finder may drink it. We do not require a Chosam (telltale seal). Here is different, for if a Nochri touched it, he would not be concerned to seal it. If he found it open, it is forbidden, lest a Nochri touched. Also R. Yerucham says so.

Question (Tosfos 23b DH Rov): What is the Chidush? A Beraisa (Kesuvos 15a) says that if meat is found, we follow the majority of stores. It connotes that this is even if it is close to a store that sells Nevelah!

Answer #1 (Rivam): One might have thought that the Beraisa is when there are two majorities, i.e. the gates of the city are not locked (and also the majority of meat outside the city is Kosher). R. Chanina teaches that we follow even a single majority. R. Zeira questioned this, but later accepted this from R. Chanina.

Objection (Ritzva): Why did he ask from a verse? He should ask from the Beraisa! Even if it is when the gates are not locked, this is only a decree mid'Rabanan [to require a second majority]!

Answer #2 (Ri): One might have thought that the Beraisa is only when it is found in the middle.

Answer #3 (Ri): R. Chanina teaches that even if it is a Kurva d'Muchach, we follow the majority.

Support (Tosfos): Regarding a barrel floating in a river, we wanted to say that Rav permits when it was found near a city that is mostly Yisraelim, for he argues with R. Chanina. How could we establish this? It seems that he permits even if it is closest to a Nochri's house, for we follow the majority of the city, like R. Chanina! Rather, surely being closest to a Nochri's house is not Muchach, since most of the city are Yisre'elim. Rav follows what is closest when it is not Muchach, unlike R. Chanina. The nearest city is Muchach , therefore he follows it. This is why the Gemara brings R. Chanina only below, regarding the barrel found in the orchard, which is Kurva d'Muchach, for it was found in an orchard of Orlah itself.

R. Ovadyah mi'Bartenura (Shekalim 7:1 DH Ma'os): The one who follows the majority even if it is further, he establishes our Mishnah to discuss when both Shofaros have the same number of Shekalim.

Mar'eh ha'Panim (on 7:1): We do not find [that either Talmud] establishes our Mishnah like this. Also, the Rambam rules like R. Chanina, and he explains our Mishnah simply! He does not rule like R. Chanina when the closeness proves that it came from the minority.

Poskim

Shulchan Aruch (YD 129:17): If a barrel of wine was floating in a river near a city that is mostly Yisraelim, if there are obstacles and a dam that would detain it if it came from elsewhere, it is permitted. We attribute only to the city nearby. If there is no dam, it is forbidden, for we attribute it to most of the surrounding [residents], who are Nochrim. If it is near a city that is mostly Nochrim, if most of the surrounding [residents] are Yisre'elim, if it could come straight without sinking, it is permitted, even if is so close to the city of Nochrim that it is Kurva d'Muchach, we abandon what is close and follow the majority.

Beis Yosef (DH u'Mah she'Chasav Nimtzeis): The Rashba says so in Toras ha'Bayis, for he explains that R. Chanina said that we follow the majority even against Kurva d'Muchach, like Tosfos says.

Shulchan Aruch (ibid.): If not, one may not benefit from the wine, and the finder may keep the barrel. If a Yisrael gave a Siman, one may even drink the wine, and it belongs to the finder. Since it is mostly Nochrim, the owner despaired.

Rema: This is only if it is sealed with a cork. If it is totally open, the wine is forbidden, lest [Nochrim] touched it.

Beis Yosef (DH u'Mah she'Chasav v'Im): The Rashba says that some say that when a Yisrael gave a Siman, one may drink it only if it has a Chosam. This is astounding. If so, what is the Chidush? This is obvious! Also, we say so only regarding one who deposits wine with a Nochri, or designates a place for it in the Nochri's house, or sent it with him. (Note: in the Rashba, it says that we require a double Chosam only for these.) If he opened and touched it, he fears being caught like a thief, he toils to seal it. If he found a Metzi'ah and opened and touched it, why would he toil to seal it? This is like a troop that entered a city in peacetime. Open barrels [of wine] are forbidden, and closed barrels are permitted.

Darchei Moshe (12): Also the Ran (Bava Metzi'a 24b DH Ba) says so. He implies that if he found it open, it is forbidden, lest a Nochri touched. Also R. Yerucham says so.

Taz (26): I forbid even if it is closed with a wooden cork Above (Sa'if 13), we say that if a troop entered a city, barrels closed with a wooden cork are forbidden, for it is normal to return a wooden cork, for it is not a toil. The Ran in Avodah Zarah says that plastering is a proof that he did not touch it. This contradicts the Rema, who forbids only if it is totally open.

Gra (40): Also Toras ha'Bayis (Sof Sha'ar 4) says so [like the Taz], and the Ran and Nimukei Yosef.