Gemara

(Beraisa): One may choose to follow Beis Shamai, or Beis Hillel;

If one follows the leniencies of both, he is wicked.

45a (Mishnah - R. Yochanan ben Nuri): If one slept on the road and it became dark, he has 2000 Amos in every direction;

Chachamim say, he has only four Amos;

45b (Rava) Question: Does R. Yochanan ben Nuri hold that Hefker objects acquire Shevisah?

i. Or, perhaps he holds that Hefker does not acquire Shevisah. A sleeping person acquires Shevisah because an awake person does.

Answer (Rav Yosef - Beraisa): If rain fell before Yom Tov, it has 2000 Amos.

i. This is unlike Chachamim. We must say that it is like R. Yochanan ben Nuri, and he holds that Hefker objects acquire Shevisah.

46a (R. Yehoshua ben Levi): The Halachah follows R. Yochanan ben Nuri.

Question: Why did R. Yehoshua ben Levi also teach that the Halachah follows the lenient opinion in Eruvin? Either of these by itself would have sufficed!

(R. Zeira): Had he taught only that the Halachah follows R. Yochanan ben Nuri, one might have thought that this is whether this is a leniency or stringency. Therefore, he taught that the Halachah follows the lenient opinion in Eruvin.

47b (Shmuel): A Nochri's property does not acquire Shevisah.

This would be no Chidush according to Chachamim! They say that Hefker, which has no owner, does not acquire Shevisah. All the more so, what has an owner [who does not acquire Shevisah] should not acquire Shevisah!

Rather, it is like R. Yochanan ben Nuri;

He holds that Hefker acquires Shevisah, for it has no owner. A Nochri's property has an owner, therefore it does not acquire Shevisah!

76a (Rabanan): If there are two houses between two Chatzeros, and each Chatzer passed through the house open to it, and put their Eruv in the other house, neither Eruv is valid;

If each house is considered a Beis Sha'ar, the Eruv cannot be placed in it;

If each house is considered a house, the people of the Chatzer must pass through a house that did not Me'arev to get to their Eruv.

Question: How is this different from Rava's law?

(Rava): If two told Levi 'make an Eruv for me', and Levi made one Eruv before Shabbos and it was eaten Bein ha'Shemashos, and he made the other Bein ha'Shemashos and it was eaten after dark, both of them are valid.

Answer: There, it is a Safek whether Bein ha'Shemashos is day or night. It is reasonable to be Machshir both Eruvin;

Here, if we consider one a house and the other a Beis Sha'ar [and vice-versa for the other Chatzer], Chachamim's words will be a mockery!

Pesachim 10a: If a weasel took a piece of Chametz and entered one of two houses checked for Chametz, and we do not know which, this is like the case of two paths:

(Mishnah - R. Yehudah): If two walked on two different paths, and only one path is Tamei, and we do not know which, and they touched Taharos:

If they ask separately, we are Metaher both of them. If they ask together, we are Metamei both.

Rishonim

Rosh (4:8): Had R. Yehoshua ben Levi taught only that the Halachah follows R. Yochanan ben Nuri, one might have thought that this is whether this is a leniency, i.e. that a sleeping person acquires Shevisah, or a stringency, that Hefker Kelim acquire Shevisah. Therefore, he taught that the Halachah follows the lenient opinion in Eruvin, i.e. we follow R. Yochanan ben Nuri only regarding people, for then it is a leniency. Hefker Kelim do not acquire Shevisah, so one may take them wherever he may go. These are not contradictory leniencies. We hold like Rabanan, that something without Da'as (understanding) does not acquire Shevisah. A sleeping person acquires Shevisah like Rashi explains. Since one who is awake acquires Shevisah, also a sleeping person acquires.

Ramban (46a DH Ha): Rashi and the Rif say that we are lenient about people like R. Yochanan ben Nuri, and about Kelim like Rabanan. Some ask that we do not rule like contradictory opinions (6b)! Rashi says that R. Yehoshua ben Levi is lenient about a sleeping person, since one who is awake acquires Shevisah. He does not rule like him about Shevisah. I disagree. No Tana says like this! R. Yochanan ben Nuri holds that a sleeping person acquires Shevisah, like Hefker. Therefore, he is stringent about Kelim. Rabanan hold that neither of these acquires Shevisah. Also, if so, why did the Gemara ask that it should have sufficed to say that the Halachah follows the lenient opinion in Eruvin? If so, we would have thought that it is because Hefker acquires Shevisah! Rather, R. Yehoshua ben Levi rules like the leniencies of both opinions. Since he can give a reason (one who is awake acquires Shevisah, just like a sleeping person), they are not considered contradictory. I say that we cannot follow contradictory leniencies regarding one person and one place. Regarding two people, we follow contradictory leniencies. If two people walked on different paths, and surely one of them became Tamei, if each asks separately, both are Tehorim (Pesachim 10a). Therefore, when someone asks about a person, we rule like R. Yochanan ben Nuri. When someone asks about Kelim, we rule like Rabanan.

Tosfos (46a DH Ka): Even had R. Yehoshua ben Levi said only "the Halachah follows the lenient opinion in Eruvin", we would be lenient like both of them (like R. Yochanan ben Nuri for people, and like Rabanan for Kelim).

Poskim

Shulchan Aruch (OC 401:1): If one slept on the road and it became dark, he has 2000 Amos in every direction. This refers to a person. Since if he were awake he would acquire Shevisah, also if he was sleeping he acquires Shevisah. Hefker items do not acquire Shevisah. One who acquires them may take them wherever he may go.

Taz (1): We say that Hefker does not acquire Shevisah, to be lenient. If it would acquire Shevisah, one who acquired it could take it only within its Techum. Sometimes a leniency can result if it acquired Shevisah, e.g. if two people acquired it at once, and they made Eruvin in opposite directions. The common area in which they may go is only close to the item. If it did not acquire Shevisah, one may take it only in the common area, like we say about two who borrowed a cloak (397:9). If it acquired Shevisah, one may take it 2000 Amos in every direction from the item. I say that in such a case, we are lenient to say that it acquired Shevisah.

Rebuttal (Eliyahu Rabah 1): Tosfos (46a DH Ka) and the Rosh say that they are not contradictory leniencies. Hefker items do not acquire Shevisah. A sleeping person acquires Shevisah, for if he were awake he would acquire Shevisah! This shows that a Hefker item never acquires Shevisah! Also, according to the Taz, the two leniencies contradict each other.

Bi'ur Halachah (DH k'Raglei): If two people acquired it at once, and they made Eruvin in opposite directions, they may not move it [outside the common area in which both of them may go]. Tosefes Shabbos, Ma'amar Mordechai and the other Acharonim say so, unlike the Taz.

Kaf ha'Chayim (4): Mishbetzos Zahav (brought below) explains that the Taz agrees that we are stringent. It seems that Be'er Heitev understood like this. (He says in the name of the Taz that we are stringent.)

Shulchan Aruch (ibid.): A Nochri's property acquires Shevisah in its place. This is a decree due to property of a Yisrael.

Taz (1): Why does the Shulchan Aruch say that a Nochri's property acquires Shevisah, due to property of a Yisrael? If two will borrow it, it can be a leniency to say that it acquired Shevisah. Since really it does not have Shevisah, this is an improper leniency! This requires investigation.

Eliyahu Rabah (2): Perhaps this law is proper! Do not say that they are contradictory leniencies. We do not say so about a decree. However, the Poskim connote that in every case it acquires Shevisah. I say that letter of the law, Kelim of Nochrim are like Hefker, like it says on 47b. Hefker does not acquire Shevisah, for we follow the lenient opinion. Here that it is a leniency to say that it acquires Shevisah, we say that the Halachah follows the lenient opinion, and it acquires. These are not contradictory leniencies, for we hold that it acquires Shevisah also when there is a stringency, due to a decree, and Chachamim wanted to make a uniform decree.

Mishbetzos Zahav: Tosefes Shabbos says that people are prone to confuse Nochri property with that of Yisre'elim, so they made it like property of Yisrael, even if a leniency results. I say that also the Taz means that if we would be lenient about Hefker, sometimes a stringency would result. It is proper that Hefker be like the one who acquires it, even if this will lead to a stringency, like the case of two who borrowed. The Taz asked according to this. Letter of the law, Nochri property is like Hefker, and it is like the one who acquires it. Two who borrowed may not move it [from their common place], even if this will lead to a leniency. How can a leniency come from a decree due to Yisrael? In any case, regarding Hefker, surely the Taz is stringent about two who borrowed [or acquired together - PF]. He merely mentioned this to ask his question [about Nochri property]. In any case, we can say that Chachamim made a uniform decree, even if a leniency results.

Tzlach (Shabbos 34a DH Tosfos): On 76a, we asked why two Eruvim [that cannot both be Kosher] is unlike Rava's law. This shows that Rava is Machshir both even if they contradict each other, i.e. the first Eruv was eaten before the latter was placed. However, if one asked about both at once, we cannot be Machshir both, for this is a contradiction. We are stringent even for mid'Rabanan laws, like Bedikas Chametz after Bitul was done. However, perhaps Chametz is more stringent, for it has a source in Torah, unlike Eruv.