Rambam - 1 Chapter a Day

Although the mitzvah per se applies only with regard to cases involving capital punishment, the prohibition applies in all cases, even with regard to matters of financial law. For this reason, it is not one of the distinctions between cases involving capital punishment and those involving financial law mentioned in the following chapter (Minchat Chinuch, mitzvah 77).

Sefer HaMitzvot (negative commandment 283) and Sefer HaChinuch (mitzvah 77) count this as one of the 613 mitzvot of the Torah. Significantly, when listing the mitzvot at the beginning of this section, the Rambam mentions only the dimension of the prohibition described in the following halachah.
With regard to that dimension of the mitzvah, the Ra’avad (in his gloss to the listing of the mitzvot at the beginning of the Mishneh Torah) objects, explaining that since the judge may ultimately change his mind, the fact that he cannot reverse his position in the debate is not sufficient to be considered as a mitzvah.

Tosefta, Sanhedrin 3:4; Jerusalem Talmud, Sanhedrin 4:7; Mechilta d’Rabbi Yishmael to the above verse.

In the Torah, the word riv, translated as “dispute,” is written in a short form, lacking a yud. This enables it to be read as rav, “great one.” According to that meaning, the verse could be interpreted “Do not respond to the great one,” i.e., do not follow his thinking blindly. Instead, weigh the matter yourself and arrive at a decision. See Halachah 6.
Alternatively, rav can be interpreted as “the majority.” In that vein, the intent of the prohibition is that if a judge sees the majority leaning in a particular direction, he should not follow without making his own decision independently (Sefer HaMitzvot, loc. cit.).

In this context, the verse could be interpreted: “Do not go against your [first] inclination in a dispute” (Radbaz).

I.e., if a judge offered a rationale for acquittal, he may ultimately decide that he made an error and hence, reverse his initial position. He may not, however, voice this concern in the debate. This measure - and the others which follow in this chapter - was instituted by the Torah as a safeguard for the rights of a defendant.
The rationale for this prohibition can be explained as follows: Since the judge cannot retract his initial opinion in the debate, even if he erred, he will seek other - and this time, more correct - rationales to support his initial concept and exonerate him [Rashi (Sanhedrin 32a)].

I.e., one of the scholars who sit before the judges (see Chapter 1, Halachah 7). As mentioned in Halachah 8, even though these scholars are not judges of the court, if one of them advances a rationale that could be used to acquit the defendant, he is included as a judge.

The Kessef Mishneh states that if, however, a judge advances an opinion holding the defendant liable and then dies, another judge is appointed before the vote is taken.

I.e., even though he has already died, when the opinions are tallied, his vote to acquit the defendant is counted.

Significantly, Sanhedrin 43a, the Rambam’s source, states this concept with regard to “one of the scholars,” and not one of the judges.

Although we desire to rule leniently and offer the defendant the maximum opportunity for acquittal, since the judge did not state his rationale, he is ignored.
It would appear that if the judge could write out his opinion, that would be significant and he would be included in the reckoning (Kin’at Eliyahu).

The intent is that the Torah uses only one prooftext to teach a rationale, and not two. Therefore if two judges each cite a different prooftext, one of them is making an error (Kessef Mishneh). See also Chapter 12, Halachah 3, where the Rambam mentions this concept.
Rav Moshe Cohen and the Siftei Cohen 25:19 protest the use of the word “even,” for it implies that certainly if they base their ruling on the same prooftext, they are counted as one. This would imply that each judge must come up with an independent rationale. That is illogical. If one judges says: “So-and-so” should be executed, because he violated the commandment: ‘Do not kill,’” there is no need for the other judges to find different rationales.

As mentioned in Chapter 11, Halachah 4, this and the principles mentioned in the following halachot also apply with regard to cases involving convictions for lashes and for exile.

As is the practice with regard to other judgments. See Chapter 11, Halachah 6.

As Chapter 11, Halachah 6, states: “With regard to [cases involving] capital punishment, we begin from the side.” As stated in Chapter 1, Halachah 3, the judges are seated in a semi-circle and the judges of the highest stature are seated in the center. Beginning from the side means asking the judge of the lowest stature to state his opinion first.

This relates to the prohibition against relying on another sage’s opinion which is mentioned in Halachah 1 (Radbaz).

Note the contrast to financial law, as mentioned in Chapter 11, Halachah 1, and Chapter 12, Halachah 3.

Sanhedrin 32b derives this concept from the oath administered to a sotah, a woman suspected of adultery. Numbers 5:19 states: “The priest administers the oath to her, saying: “...If a man did not lie with you... you will be held blameless by these waters.” Although the oath then continues to mention the severe punishment the woman will suffer if she transgressed, it begins with reassurance if she is innocent. The same pattern is followed here.

This refers to the students who sit in observation of the court proceedings, as stated in Chapter 1, Halachah 7.

One of the fundamental points of the Torah’s approach to capital punishment is that ultimately man’s future is in God’s hands. The court must do what it can to judge the matter, but it need not work overzealously to convict the defendant, for even if he is not executed by the court, God will administer justice (see Sanhedrin 37b). Hence, even though there is a possibility that the student’s rationale would be substantial, since he is not a judge, he is not given a chance to decide the defendant’s fate. Indeed, he is not even given the opportunity to state his point.

I.e., to participate in the debate.

But instead becomes part of the court. Kin’at Eliyahu states that it would appear that another judge is also added to the court together with him, so that there will not be the possibility of an evenly balanced court. He also questions what will happen in the future, for the court will have an extra judge.

For that would be embarrassing for him.

The Lechem Mishneh (and similarly, many commentaries to Sanhedrin 40a, the Rambam's source) maintain that this phrase is an error. The intent is that his opinion is considered. He himself is not considered a judge, for a relative - and certainly, the defendant himself - cannot serve as a judge.

Sanhedrin 33b derives this concept from the adjuration (Exodus 23:7): “Do not execute the guiltless or the righteous.” Implied is that if he is innocent, even if he was not deemed righteous by the court, he should not be executed.

As Sanhedrin, loc. cit., continues: If he was deemed righteous, even though he is not innocent, he should not be executed.

The Sadducees were followers of Tzadok, one of the students of Antigonus of Socho, who abandoned traditional Jewish practice and started a new sect. Although their intent was to assimilate among the Greek and Roman societies, they professed to maintain adherence to Judaism and disguised their assimilationist tendencies by protesting that it is only to the Oral Law that they were rejecting. The Written Law, by contrast, they would agree to keep. If a matter was thus accepted by the Sadducees, it is quite obvious and everyone would realize the error. Hence, the judgment is discarded. If, however, the judgment was not a point accepted by the Sadducees, even though it concerns an explicit statement of the Mishnah, the error is not as obvious, and the judgment is allowed to stand.

When speaking about the prohibition against forbidden sexual relations, a plural term, mishkavei ishah, is used in Leviticus 20:13, indicating that there are two types of forbidden intercourse, vaginal and anal (Sanhedrin 54a). Horiot 4a states that even the Sadducees would accept this concept.

I.e., without inserting the entire organ. According to Sanhedrin 33b, this is considered as intercourse. Nevertheless, this point is not accepted by the Sadducees. See Hilchot Issurei Bi'ah 1:10 and commentaries.