Unanimous Juries in Louisiana - Unanimous Verdicts in the Talmud
אמר רב כהנא סנהדרי שראו כולן לחובה פוטרין אותו מ"ט כיון דגמירי הלנת דין למעבד ליה זכותא והני תו לא חזו ליה

Rav Kahana says: In a Sanhedrin where all the judges saw fit to convict the defendant in a case of capital law, they acquit him. The Gemara asks: What is the reasoning for this halakha? It is since it is learned as a tradition that suspension of the trial overnight is necessary in order to create a possibility of acquittal. The halakha is that they may not issue the guilty verdict on the same day the evidence was heard, as perhaps over the course of the night one of the judges will think of a reason to acquit the defendant. And as those judges all saw fit to convict him they will not see any further possibility to acquit him, because there will not be anyone arguing for such a verdict. Consequently, he cannot be convicted.

(א) סַנְּהֶדְרִין שֶׁפָּתְחוּ כֻּלָּם בְּדִינֵי נְפָשׁוֹת תְּחִלָּה וְאָמְרוּ כֻּלָּן חַיָּב הֲרֵי זֶה פָּטוּר עַד שֶׁיִּהְיוּ שָׁם מִקְצָת מְזַכִּין שֶׁיְּהַפְּכוּ בִּזְכוּתוֹ וְיִרְבּוּ הַמְחַיְּבִין וְאַחַר כָּךְ יַהֲרֹג:

When all the judges of a Sanhedrin begin their judgment of a case involving capital punishment and say that the defendant is liable, he is exonerated. There must be some who seek to exonerate him and argue on his behalf, but yet the majority hold him liable. Only then he is executed.

Rabbi Zvi Hirsch Chajes, Commentary to Sanhedrin 17a

... A judge on the Sanhedrin must be a brilliant thinker. In fact, the Talmud elbaorates that before gaining entry onto the bench, a Sanhedrin judge must show that he is capable of providing a cogent, logical argument for an impossible factual scenario. The judge must prove that a certain dead animal, ritually impure according to the Torah, is actually reitually pure according to Torah law. We learn therefore that the Sanhedrin has the responsibility to make the impossible argument in favor of the defendant. When a Sanhedrin unanimously convicts a defendant, collusion must be suspected. Since a verdict is reached without any dissenting opinion, the judges on the Sanhedrin are not doing their job properly, as they are failing to make the "impossible arguments". As such, the Sanhedrin's unanimity is suspect, and the verdict is dismissed.

Aruch HaShulchan, Choshen Mishpat 18:7

...Since all the judges found him guilty, none found any aspects of merit in his case. Yet, we do not execute a defendant without a proper search for merit, for it is through argumentation that the facts most clearly emerge...

Rabbi Judah Loewe, quoted from "Guilt: Henry Friendly Meets the MaHaRaL of Prague", Rosenberg & Rosenberg, 1991

The function of the Sanhedrin is to search for "evidence of innocnece rather than guilt.... they should not be so concerned about punishing those who have committed a wrong. The court should stick to its business of finding merit in the defendant's cause....Preserving the court's role as a righteous court that seeks to free the innocent is more important than the incidental fact of the defendant's factual guilt. That we sometimes free guilty people is not significant. What is critical is preserving the character of the court."

Rav Mendachem Mendel Schneerson, from "The Unanimous Verdict According to the Talmud," Ephraim Glatt, 2013

Since punishment is meant to help cleanse a defendant's soul, a defendant whose crimes are exceptionally egregious does not deserve to be punished. Rather, he must walk free, leaving his punishment in the hands of the Lord - surely a worse fate. Likewise, explains Schneerson, a defendant unanimously convicted is undeserving of punishment by the hands of mere mortals. Instead, this heinous criminal must be judged by the Master Judge, ie God. Thus, this perplexing Talmudic statement is actually quite rational.