- Who chooses the three דיינים for a Beis Din?
The third Perek begins by discussing the selection of three judges for monetary cases: זה בורר לו אחד וזה בורר לו אחד – this litigant chooses himself one and that litigant chooses himself one, ושניהן בוררין להן עוד אחד – and they both choose one more for themselves, according to Rebbe Meir. The Chochomim say: שני דיינין בוררין להן עוד אחד – the two judges choose one more for them. The Gemara ultimately clarifies that each בעל דין chooses one judge, and the Tannaim argue if the third judge is selected jointly by the בעלי דין, or by the judges. The Gemara suggests their argument concerns Rav’s principle, that witnesses do not sign a שטר unless they know with whom they sign (because if one witness is found ineligible, the entire testimony is disqualified, which embarrasses the valid witnesses). Similarly, these Tannaim would argue if the two judges must consent to the third judge. However, the Gemara concludes that all may agree with Rav’s principle, and the third judge requires the other judges’ consent. Their argument is whether דעת בעלי דינין - the litigants’ consent is also required.
- The machlokes about a בעל דין disqualifying a judge
In the Mishnah, Rebbe Meir said: זה פוסל דיינו של זה וזה פוסל דיינו של זה – this litigant can disqualify the judge [chosen by] that litigant, and that litigant can disqualify the judge [chosen by] this litigant. The Chochomim say one must provide proof to disqualify a judge. The Gemara wonders how Rebbe Meir allows a בעל דין to simply disqualify a judge, and Rebbe Yochanan explains: בערכאות שבסוריא שנו – they taught this law regarding courts of Suria, whose judges were not experts in Torah law but appointed by public consent. Either בעל דין can refuse such a judge and insist on a knowledgeable one, but he cannot reject מומחים – experts. When the Chochomim said that one cannot disqualify judges who are "כשרין או מומחין מפי בית דין" – eligible or certified experts (implying Rebbe Meir holds one can disqualify a מומחה), they meant that all eligible judges are נעשו כמומחין מפי בית דין – considered like certified experts and cannot be disqualified. When the Chochomim told Rebbe Meir that one cannot disqualify a judge "שמומחה לרבים" – who is a publicly known expert, they meant a judge שהמחוהו רבים עליהם – that the public authorized over themselves, but is not a מומחה.
- Machlokes about a בעל דין disqualifying a witness
The Gemara challenges Rebbe Yochanan’s assertion that Rebbe Meir agrees an expert judge cannot be disqualified, because eligible witnesses are the equivalent of expert judges, yet Rebbe Meir said in the Mishnah: זה פוסל עדיו של זה וזה פוסל עדיו של זה – this [litigant] can disqualify that one’s witnesses, and that [litigant] can disqualify this one’s witnesses!? Reish Lakish said: פה קדוש יאמר דבר זה – Would Rebbe Meir’s holy mouth say such a thing?! Rebbe Elazar ultimately explains: בבא הוא ואחר לפוסלן – the case is where [the בעל דין] and another witness came to invalidate [the other בעל דין’s witnesses]. The Gemara asks that the בעל דין is נוגע בעדותו – partial in his testimony, since it directly impacts his case!? Two answers are given: (1) The בעל דין and his accompanying witness testified to a witness’s disqualification based on פגם משפחה – a blemished lineage, such as descending from slaves. Rebbe Meir holds they are testifying about his family, and the witness is disqualified along with them, and the Rabbonon respond that he is still נוגע בעדות. (2) The case is where the opposing בעל דין claims to have two sets of witnesses, and the Tannaim argue if צריך לברר – he must corroborate his claim, which the Gemara proceeds to explain.