Sanhedrin, chapter 3, Mishnah 7. The mishnayos gradually advance in describing the court procedures: accepting testimony, the deliberation between the judges, and now - the next stage, delivering the verdict to the litigants.
"Gamru es hadavar - hayu machnisin osan":
Once the judges finished their deliberations and decided how to rule, they would bring the litigants back in. The Mishnah did not say this explicitly, but it emerges from here that after gathering the information, when the deliberation between the judges began (which was discussed in the previous Mishnah), the litigants were taken out of the room, and now they are brought back in.
"Hagadol shebadayanim omer":
The verdict is delivered by the senior judge of the three, and there are two reasons for this:
The honor of the leading sage, the greatest of the sages sitting in judgment.
It is human nature to assume that whoever delivers the judgment is acting maliciously against him. When it is known in advance that the greatest of the judges is the one who delivers the verdict, regardless of the positions taken by the other judges, it appears as a fixed, procedural process. But if a specific judge is the one delivering the judgment, the losing side will assume that that judge sought to do so out of malice, and resentment will arise from this.
The commentators disagree as to which of the reasons is the primary one, and there is a major practical difference: according to the first reason, the greatest judge may pass his honor to another if he so wishes; whereas according to the second reason, the honor may not be transferred, because this would undermine the principle, lest the losing litigants assume that the judge acted maliciously against them. The Tur cites the latter opinion, and therefore specifically the senior member is the one who delivers the verdict.
And so the Mishnah continues: "Ish ploni atah zakai, ish ploni atah chayav" - the judge issues the ruling and notifies each side whether a payment obligation is imposed on him or not.
"Lichsheyeitzei echad min hadayanim lo yomar":
The Mishnah asks: "Uminayin lichsheyeitzei echad min hadayanim lo yomar: Ani mezakeh vachaverai mechayevin, aval mah e'eseh shechaverai rabu alai" - from where do we know that it is forbidden for a judge, upon leaving the court, to tell the litigant that he himself found him innocent, while his two colleagues found him liable and they are the majority that ruled against him?
Two verses are brought for this in the Mishnah:
"Lo telech rachil be'amecha" - this is the Torah's prohibition of gossip. The definition of gossip is specific and exact: telling a person what a third person said about him. Reuven who says to Shimon, "Do you know what Levi said about you?" - this is gossip. It makes no difference whether the words are true or false, and even if they are words of praise (such as a child telling his friend that someone said about him that he excels in math) - the matter is forbidden. This prohibition applies to everyone, and not only to judges. And this is exactly what is done here: the judge reveals to the litigant that his two colleagues are the ones who spoke against him, whereas he did not.
"Holech rachil megaleh sod" - a verse in Mishlei, and this is not an explicit d'Oraisa prohibition, but a prohibition of revealing a secret and exposing the secrets of others. Information that is meant to remain private, whether for good or for bad, may not be exposed without the consent of its owner, for a person has a right to privacy. Here too: the deliberation between the judges took place behind closed doors, and a judge has no permission to reveal who found him liable and who found him innocent.
It is worth noting that there are different versions of the Mishnah text: some bring one verse and some bring the other, while the version before us brings both. The Shulchan Aruch brings the latter verse, regarding revealing a secret, but both reasons are correct, and both apply not only to judges but to every person.
In summary: In this Mishnah we learned about the stage of delivering the verdict - bringing the litigants back in after the conclusion of the deliberation, and delivering the ruling specifically through the greatest among the judges, both out of respect for him and to prevent resentment. We also learned about the prohibition against a judge revealing his personal stance during the deliberation, a prohibition derived from two verses: "You shall not go around as a talebearer among your people" and "A talebearer reveals secrets" - two prohibitions that apply to each and every person, and not only to judges.