Sanhedrin 40a: If a court of 23 is judging a case, 11 say innocent, 11 say guilty, and 1 says, “I don’t know,” or even if 22 of them say innocent or guilty and 1 says, “I don’t know,” they must add judges. And how many do they add? Two at a time, until they reach 71.
סנהדרין מ ע”א: אחד עשר מזכין ואחד עשר מחייבין. ואחד אומר איני יודע, ואפילו עשרים ושנים מזכין או מחייבין ואחד אומר איני יודע ־ יוסיפו הדיינין. וכמה מוסיפין ־ שנים שנים, עד שבעים ואחד.
Rav Chaim Kreiswirth was once sitting on a beis din when he realized that the other two dayanim were going to pasken wrongly. If he voted against them, he would be overruled. Therefore, he said, “I must admit that I don’t know who is right and who is wrong here. Maybe you can explain to me how you are so certain?” As much as they tried, they could not convince him; he insisted that he didn’t know. This forced them to bring in two more dayanim.
According to the Rambam Hilchos Sanhedrin 8:2, the one saying “I don’t know” is still part of the beis din, so you have the original 2, the new 2, and the “I don’t know” for a total of 5. (But this time, if at least 3 dayanim agree on a psak, even if one or both of the other 2 say “I don’t know”, we follow the majority.) In this case, Rav Kreiswirth must have been hoping that both of the new dayanim would take his side, and then he too would reveal his true opinion.
Source: Mayim Chaim p. 168
[The question of whether it is allowed for a dayan to lie and say “I don’t know” as a tactic is discussed by the Pischei Teshuva Choshen Mishpat 18:5. He brings that this was a dispute between the Beis Yaakov (15) and the Shvus Yaakov (1:138). The Beis Yaakov held it is forbidden, because this would embarrass the whole beis din by making it seem that they are unlearned. But the Shvus Yaakov held it is permitted in order to bring about true justice. The Pischei Teshuva quotes a compromise opinion, the Birkei Yosef, who says that the Shvus Yaakov is correct only in the particular case he was asked about, when a rav was called to judge a dispute together with two ignorant people (“yoshvei kranos”). But when the other two judges are learned and qualified people, the third has no right to lie and subvert their psak. He must declare his true opinion and let the halacha be decided by the majority, as the Torah commands.
Since we can assume that Rav Kreiswirth sat on a beis din with qualified talmidei chachomim, it must be that he held like the Shvus Yaakov in all cases, not just with ignoramuses.
Incidentally, Rabbi Akiva Tatz uses this Pischei Teshuva to make the point that one can harm another person with his free will even if the harm was not decreed by Hashem. The only exception is when the harm is being carried out by a beis din; in that case, Hashem stands with the beis din and whatever they decide must have been His will. That is why in the case of a qualified beis din, the dissenting dayan should speak the truth and let the majority decide against him: even if he is halachically correct, the beis din’s psak must have been Hashem’s will. But a beis din of ignoramuses or colluders is not a beis din at all, and it’s his duty to stop them from harming the litigant using any method available to him.
Similarly, the Chinuch (Mitzvah 524, Edim Zomemim) quotes the halacha that if the beis din has already executed a man based on the false testimony, the witnesses are not punished. He explains: “For G-d stands among the dayanim, and if the accused had not been liable to die due to other sins he committed, he would not have been convicted.” It is clear from the Chinuch that this is true only of someone executed by beis din, but a regular murder victim might die despite not deserving it, simply because of the free will of the murderer.]
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