Gemara

(Rav Nachman): If Reuven and Shimon each claimed 'I inherited this land (or ship) from my fathers', Kol d'Alim Gavar.

Question: Why is this different than two documents with the same date? There, Rav says that the bearers split the property, and Shmuel says that we apply Shuda (it is left to the judges' discretion)!

Kesuvos 93b: Rav holds like R. Meir, who says that the signatures on a document empower it (it does not matter which was given first). Shmuel holds like R. Elazar, who says that the witnesses who see a document given to the recipient empower it. (The first one given is valid.)

Answer: There, we will never know which document was given first. Here, perhaps one will bring witnesses later (we do not want to give a ruling that might be overturned later).

Question: Why is this different than the following?

(Mishnah): If Levi traded sold his slave to Shimon (in her absence), and they argue about whether she gave birth before or after the sale, they divide the value of the child.

62b (Rav): If the seller defined the borders in three directions, the buyer acquires everything between them, but not the fourth border;

(Shmuel): He also acquires the fourth border.

Some say that Rava ruled that he acquires the fourth border. Some say that he rules that he does not get it. These versions argue about when the fourth border is between the other borders, and there are date trees on it or it is nine Kavim; or, if the fourth border is not between the other borders, and there are not date trees on it and it is not nine Kavim. We apply Shuda of judges.

Kesuvos 93b: Rami bar Chama's mother wrote her property to him in the morning. In the afternoon, she wrote it to Mar Ukva bar Chama. Rami went to Rav Sheshes, who gave the property to him. Mar Ukva went to Rav Nachman, and he ruled in his favor.

Rav Sheshes: I gave it to Rami because his document was earlier.

Rav Nachman: This matters only in Yerushalayim (where they write the hour in the document)! The Halachah is Shuda. I ruled based on my Shuda.

Rav Sheshes: My ruling may also be considered Shuda!

Rav Nachman: No. I am a judge, but you are not. Also, your ruling was not intended to be Shuda.

Gitin 14b (Beraisa - Chachamim of Bavel): If Reuven said 'take 100 Zuz to Ploni', and Ploni died before the Shali'ach arrived, and Reuven died, the Shali'ach does what he wants (he gives it to Reuven's heirs or Ploni's heirs).

They hold that the best solution is Shuda of the Shali'ach.

Kidushin 74a (Beraisa): If the parties are no longer in front of the judge, he is not believed to say who won the case and who must pay.

Question: He should judge them again!

Answer: The case is, the verdict was based on Shuda.

Rishonim

Rif and Rosh (Kesuvos 53b and 10:13): Rav and Shmuel discuss documents for land, e.g. purchases or gifts. If they were admissions or loans, a Mishnah (93b) teaches that they divide the money.

Rebuttal (Ran 53b DH Aval): Perhaps Shuda applies even to loans. The Stam Mishnah is R. Meir, therefore it says they divide! Also, the Mishnah does not discuss Shuda at all. It teaches only how to divide, e.g. in a case when all agree that Shuda does not apply and they divide, e.g. they are for the same hour, or a Shali'ach acquired at once for many recipients!

Rif and Rosh (Kesuvos 45b and 9:11): Regarding sales and gifts, the Halachah follows Shmuel (Shuda).

Hagahos Ashri: Some suggested using Shuda when there is a Machlokes. They should not. Shuda applies only to an expert judge who is Gadol ha'Dor. Rav Nachman said that Rav Sheshes is not qualified! We apply Shuda only where the Gemara said. Where it was not said, ha'Motzi mi'Chavero Alav ha'Re'ayah. However, R. Baruch said that Rav Nachman said 'since I was authorized by the Reish Galusa, your Shuda is invalid in place of mine.' Otherwise, any judge can use Shuda.

Rambam (Hilchos Zechiyah 5:6): If there are two sale or gift documents for a field, and the dates are the same, if it is not the practice to write the hour on the document, it is left to the judges' discretion. Whomever they lean to leave the field with, he keeps it.

Rosh (10:13 and Bava Basra 3:23): The Rashbam says that Shuda is giving to whom it seems that the giver wanted to give it to. R. Tam says that the judge gives it to whomever he wants, without any reason, as long as he does not benefit. If he benefits, he is not a judge. He learns from Gitin. The Shali'ach gives it to whom he wants, and the Gemara calls this Shuda of judges. (see ozvh Bava Basra Note: our Gemara says just 'Shuda'.) Another proof is from Kidushin. If Shuda were based on reasons, the judge could judge them again and reach the same decision! Rather, it is the judge's whim without any reason. Perhaps before he wanted to give it to Ploni, and if he judges again, he will decide to give it to Almoni. Also, in Kesuvos, Rav Nachman did not accept Rav Sheshes' Shuda. If it depends on reasons, surely Rav Sheshes could judge this! Rather, it is the judge's whim, and Rav Nachman was an expert judge appointed by the exilarch, so he could give to whom he wants. The Yerushalmi says so. R. Chananel cites a tradition that Shuda applies only to land, and to expert judges. Rav Nachman said that Rav Sheshes cannot judge by Shuda, even though he was a great Chacham. It seems that it applies also to Metaltelim, like the case of the Shali'ach, which our Gemara calls Shuda. Presumably, R. Chananel refers to Shuda of judges, but Shuda of a Shali'ach applies even to Metaltelim.

Hagahos Ashri: Nowadays, division is better, like Rav. We do not do Shuda.

Poskim

Shulchan Aruch (CM 240:3): If there are two sale or gift documents for a field, and the dates are the same, it is left to the judges' discretion. Whomever they lean to leave the field with, he keeps it.

Beis Yosef (DH Shnei and DH u'Mah she'Chosav Rabeinu v'Chosav): Rashi says that Shuda is estimating to whom he wanted to sell the property. R. Tam says that the judges give it to whomever they want. The Rosh (107:6 DH Od) supports this from the Yerushalmi (10:4).

Darchei Moshe (3*): Moharam (241) says that Shuda applies only to an expert judge who is Gadol ha'Dor, and only when the Gemara said so. When it did not say so, ha'Motzi mi'Chavero Alav ha'Re'ayah. The Ran (Shevuos 13b DH Tanya) and Nimukei Yosef (Bava Basra 18a) say that some texts say Shochda of judges, for they may take a bribe, since it is left to their desire. This is like Tosfos. Rashi holds that they must determine to whom the giver wanted to give it, so it is like other judgments. However, Tosfos says that if he took a bribe, his ruling is invalid.

SMA (12): The Shulchan Aruch means 'whomever the judges think that he wanted to give or sell the property.' This is why the Rema calls this Shuda of judges.

Shach (4): Also the Tur explained like Rashi. Why did he go against the Rosh, who holds like R. Tam? Surely, the Ran and Nimukei Yosef do not permit taking a bribe. It is an exaggeration They merely mean that this is like a bribe The Ramban (35a) explicitly says so.

Rema: Some say that Shuda of judges applies only to expert judges, and regarding land. Some say that it applies even to Metaltelim, if no one is Muchzak in them.

Shach (5): This requires investigation nowadays. (The Rema (3:2) says that nowadays there is no expert judge who may judge alone.)

Gra (17): The Rashbam (Sof 35a) explains that the Gemara asked why Rav Nachman's law is unlike the sale of the pregnant slave. Had it challenged Shmuel, the Gemara in Kesuvos would have challenged him, for that is the primary place he said his law. It did not challenge Shmuel because Shuda applies only to land