Mdthbs

Sanhedrin 1:6 explains the size of the small sanhedrin, but I'm having trouble following the reasoning. It says (my notes in brackets):

From where do we learn that the little Sanhedrin should be made up of twenty three? As it says, “The assembly shall judge”, “The assembly shall deliver” (Num. 35:24-25), an assembly that judges and an assembly that delivers, thus we have twenty. [Discussion of how we know an assembly is 10.] And from where do we learn that we should bring three others [to the twenty]? By inference from what it says, “You shall not follow after the many to do evil” (Ex. 23:2), I conclude that I must be with them to do well. [Discussion about needing a majority of two to convict but only one to acquit.] The court must not be divisible equally, therefore they add to them one more; thus they are twenty three.

In other words: we start with 20, and we have to add to get an odd number, and we get a side discussion of needing a majority of two to convict -- but I don't see how that adds up to 23 when they could just add one judge to get to 21.

It looks like the interpretation hinges on "by inference from 'you shall not follow after the many to do evil'", but since there are already "many" (well, 20), I don't see how to read that as "add three more". I didn't find clarification in the g'mara.

What is the mishna's logic for adding three judges to the two assemblies of ten?

My understanding of the Mishnah is as follows:

The court must contain at least 20 members because the court must be able to simultaneously contain an "assembly" of convicters and an "assembly" of pardoners. If it didn't need to have the potential for both simultaneously then we shouldn't need 20 to begin with – e.g. a court of 15 can still put forth an "assembly" of convicters or an "assembly" of pardoners (such as if the votes are split 10-5).

The Mishnah then adds a twist to this by telling us that even though an "assembly" is technically 10 people, in order for the convicters to win they have to outnumber the pardoners by at least two. Therefore, we need to add two more judges. We can't take these two judges from the existing judges because then there is no possibility of having simultaneous "assemblies" of convicters and pardoners (which if unnecessary should mean that we never need 20 judges to begin with).

However, now that there are 22 judges it leaves the possibility of an evenly split court, which we can't have. We can't take away one judge, because then we would be one short either for the "assembly" of convicters or the "assembly" of pardoners. Therefore we have to add yet another judge, bringing the total to 23.

Note also that Rambam when codifying this law states that it's more of a tradition than actually based on the cited verses:

Hilchot Sanhedrin 5:3

ומניין שאין דנין דיני נפשות אלא בעשרים ושלשה אע"פ שדברי קבלה הן הרי הוא אומר ושפטו העדה והצילו העדה עדה שופטת ועדה מצלת עדה שופטת והן המחייבין ועדה מצלת והן המזכין ואין עדה פחות מעשרה הרי עשרים ומוסיפין שלשה כדי שלא יהא בית דין שקול ויהיה בו אחרי רבים להטות

What is the source which teaches that capital cases may be judged only by a court of 23? Although this is a matter conveyed by the Oral Tradition, there is an allusion to it in the Torah. Numbers 35:24-25 states: "And the congregation shall judge... and the congregation shall save...." Implied is that there must be the possibility of a congregation judging - and condemning him to death - and a congregation saving - and seeking his acquittal. Now a congregation is no less than ten. Thus there are at least 20 judges. We add three judges so that there not be an equally balanced court and to allow the possibility of "following after the inclination of the majority."

(Touger translation, my emphasis)