Halacha

הלכה א
אֶחָד מִן הַדַּיָּנִים בְּדִינֵי נְפָשׁוֹת שֶׁהָיָה מִן הַמְזַכִּין אוֹ מִן הַמְחַיְּבִין לֹא מִפְּנֵי שֶׁאָמַר דָּבָר הַנִּרְאֶה לוֹ בְּדַעְתּוֹ אֶלָּא נָטָה אַחַר דִּבְרֵי חֲבֵרוֹ הֲרֵי זֶה עוֹבֵר בְּלֹא תַּעֲשֶׂה. וְעַל זֶה נֶאֱמַר (שמות כג ב) "וְלֹא תַעֲנֶה עַל רִב לִנְטֹת". מִפִּי הַשְּׁמוּעָה לָמְדוּ שֶׁלֹּא תֹּאמַר בִּשְׁעַת מִנְיָן דַּי שֶׁאֶהֱיֶה כְּאִישׁ פְּלוֹנִי אֶלָּא אֱמֹר מַה שֶּׁלְּפָנֶיךָ:
כסף משנה
1.
When one of the judges in a case involving capital punishment rules to acquit the defendant or to hold him liable, not because this is his own opinion which he arrived upon the basis of his own decision, but rather he was swayed after his colleague's words, he commits a transgression, as implied by Exodus 23:2: "Do not respond to a dispute with an inclination." According to the Oral Tradition, this command is interpreted to mean that, when the judges are determining the verdict, a person should not say: "It is sufficient for me to adopt so-and-so's understanding." Instead, he should say what he thinks himself.

הלכה ב
וּבִכְלַל לָאו זֶה שֶׁלֹּא יַחְזֹר הַמְלַמֵּד זְכוּת בְּדִינֵי נְפָשׁוֹת לְלַמֵּד חוֹבָה שֶׁנֶּאֱמַר (שמות כג ב) "לֹא תַעֲנֶה עַל רִב לִנְטֹת". בַּמֶּה דְּבָרִים אֲמוּרִים בִּשְׁעַת מַשָּׂא וּמַתָּן. אֲבָל בִּשְׁעַת גְּמַר דִּין יֵשׁ לַמְלַמֵּד זְכוּת לַחְזֹר וּלְהִתְמַנּוֹת עִם הַמְחַיְּבִים:
כסף משנה
2.
Included in this interdiction is a prohibition against a judge who had proposed a rationale to exonerate a defendant in a capital case to propose a rationale to convict him. This is also implied by: "Do not respond to a dispute with an inclination."
When does the above apply? In the give and take among the judges. At the time of the verdict even a judge who had proposed a rationale for acquittal may join the others who vote for conviction.

הלכה ג
תַּלְמִיד שֶׁהָיָה מְזַכֶּה וּמֵת רוֹאִין אוֹתוֹ כְּאִלּוּ הוּא מְזַכֶּה בִּמְקוֹמוֹ:
כסף משנה
3.
When a scholar offers a rationale for acquittal and then dies, we consider it as if he is alive and advocating this position.

הלכה ד
אָמַר אֶחָד יֵשׁ לִי לְלַמֵּד עָלָיו זְכוּת וְנִשְׁתַּתֵּק אוֹ מֵת קֹדֶם שֶׁיְּלַמֵּד זְכוּת וְיֹאמַר מֵאֵי זֶה טַעַם מְזַכֶּה הֲרֵי הוּא כְּמִי שֶׁאֵינוֹ:
כסף משנה
4.
If a judge says: "I can offer a rationale to acquit him" and then lost the power of speech or died before he could explain the rationale for acquittal, it is as if he does not exist.

הלכה ה
שְׁנַיִם שֶׁאָמְרוּ טַעַם אֶחָד אֲפִלּוּ מִשְּׁנֵי מִקְרָאוֹת אֵין נִמְנִין אֶלָּא כְּאֶחָד:
כסף משנה
5.
When two judges mention one rationale, even if they cite different prooftexts, they are only counted as one.

הלכה ו
וּמִפִּי הַשְּׁמוּעָה לָמְדוּ שֶׁאֵין מַתְחִילִין בְּדִינֵי נְפָשׁוֹת מִן הַגָּדוֹל שֶׁמָּא יִסְמְכוּ הַשְּׁאָר עַל דַּעְתּוֹ וְלֹא יִרְאוּ עַצְמָן כְּדָאִין לַחְלֹק עָלָיו. אֶלָּא יֹאמַר כָּל אֶחָד דָּבָר הַנִּרְאֶה לוֹ בְּדַעְתּוֹ:
כסף משנה
6.
According to the Oral Tradition, we learned that with regard to cases involving capital punishment, we do not ask the judge of the highest stature to render judgment first, lest the remainder rely on his opinion and not see themselves as worthy to argue against him. Instead, every judge must state what appears to him, according to his own opinion.

הלכה ז
וְכֵן אֵין פּוֹתְחִין בְּדִינֵי נְפָשׁוֹת לְחוֹבָה אֶלָּא לִזְכוּת. כֵּיצַד. אוֹמְרִים לָזֶה שֶׁחָטָא אִם לֹא עָשִׂיתָ דָּבָר זֶה שֶׁהֵעִידוּ בּוֹ עָלֶיךָ אַל תִּירָא מִדִּבְרֵיהֶם:
כסף משנה
7.
Similarly, with regard to cases involving capital punishment, we do not begin with a condemnatory statement, but rather one which points towards acquittal.
What is implied? We tell the presumed transgressor: "If you did not commit the transgression concerning which testimony was given concerning you, do not fear the words of the witnesses.

הלכה ח
אָמַר אֶחָד מִן הַתַּלְמִידִים בְּדִינֵי נְפָשׁוֹת יֵשׁ לִי לְלַמֵּד עָלָיו חוֹבָה מְשַׁתְּקִין אוֹתוֹ. אָמַר יֵשׁ לִי לְלַמֵּד עָלָיו זְכוּת מַעֲלִין אוֹתוֹ עִמָּהֶן לַסַּנְהֶדְרִין. אִם יֵשׁ מַמָּשׁ בִּדְבָרָיו שׁוֹמְעִין לוֹ וְאֵינוֹ יוֹרֵד מִשָּׁם לְעוֹלָם. וְאִם אֵין מַמָּשׁ בִּדְבָרָיו אֵינוֹ יוֹרֵד מִשָּׁם כָּל הַיּוֹם כֻּלּוֹ. אֲפִלּוּ אָמַר הַנִּדּוֹן עַצְמוֹ יֵשׁ לִי לְלַמֵּד עַל עַצְמִי זְכוּת שׁוֹמְעִין לוֹ וְעוֹלֶה לְמִנְיָן. וְהוּא שֶׁיִּהְיֶה מַמָּשׁ בִּדְבָרָיו:
כסף משנה
8.
When one of the scholars makes a statement with regard to a case involving capital punishment: "I can teach a rationale which would convict him," we silence him. If he states: "I can teach a rationale which will exonerate him," he is raised up and included in the Sanhedrin. If his words are of substance, we heed his statements and he never descends. If his words are not of substance, he does not descend from the court for that entire day.
Even if the defendant himself says: "I can teach a rationale which will exonerate myself," we heed his statements and he is counted among the judges, provided his words are of substance.

הלכה ט
בֵּית דִּין שֶׁטָּעוּ בְּדִינֵי נְפָשׁוֹת וְחִיְּבוּ אֶת הַפָּטוּר וְגָמְרוּ דִּינוֹ לְחוֹבָה וְנִרְאֶה לָהֶם הַטַּעַם שֶׁיִּסְתְּרוּ בּוֹ אֶת דִּינוֹ כְּדֵי לְזַכּוֹתוֹ סוֹתְרִין וְחוֹזְרִין וְדָנִין אוֹתוֹ. אֲבָל אִם טָעוּ וּפָטְרוּ אֶת הַמְחֻיָּב הֲרִיגָה אֵין סוֹתְרִין אֶת דִּינוֹ וְאֵין מַחֲזִירִין אוֹתוֹ. בַּמֶּה דְּבָרִים אֲמוּרִים בְּשֶׁטָּעוּ בְּדָבָר שֶׁאֵין הַצְּדוֹקִין מוֹדִין בּוֹ. אֲבָל אִם טָעוּ בְּדָבָר שֶׁהַצְּדוֹקִין מוֹדִין בּוֹ מַחֲזִירִין אוֹתוֹ לְחוֹבָה. כֵּיצַד. אָמְרוּ הַבָּא עַל הָעֶרְוָה שֶׁלֹּא כְּדַרְכָּהּ פָּטוּר וּפְטָרוּהוּ מַחֲזִירִין אוֹתוֹ וּמְמִיתִין אוֹתוֹ. אֲבָל אִם אָמְרוּ הַמְעָרֶה שֶׁלֹּא כְּדַרְכָּהּ פָּטוּר וּפְטָרוּהוּ אֵין מַחֲזִירִין אוֹתוֹ. וְכֵן כָּל כַּיּוֹצֵא בָּזֶה:
כסף משנה
9.
When a court errs with regard to a case involving capital punishment and convict an innocent person, ruling that he is guilty, and later they discover a rationale that would require that the ruling be nullified and he be vindicated, they nullify the ruling and retry the case. If, however, they erred and acquitted a person liable to be executed, the judgment is not nullified and the case is not retried.
When does the above apply? When they erred with regard to a matter that the Sadducees would not acknowledge. If, however, they erred with regard to a matter that the Sadducees acknowledge, we retry the case to convict him.
What is implied? If they said that a person who has adulterous or incestuous anal intercourse is not liable and they released him, he is retried and executed. If, however, they said a person who merely entered the woman's anus with the crown of his organ is not liable, and they released him. He is not retried. Similar principles apply in all analogous situations.

שופטים הלכות סנהדרין והעונשין המסורין להם פרק י
Shoftim Sanhedrin Chapter 10