Sanhedrin 19a - Distinction Between Kings from Yehuda and Yisroel

The Mishna says that a king cannot judge nor can he be judged. The gemara explains that since he cannot be judged due to a lack of respect for him, he cannot judge. But, the gemara makes a distinction between Kings of Yisroel and Kings of beis David. The Mishna that doesn't allow for a king to be judged is speaking about a king of Yisroel who cannot be judged because of the catastrophic story that occurred with Yanai and Shimon Ben Shetach, but a king from beis david can be judged therefore he can judge.

Tosafos limits the allowance for kings of beis david to judge. They can only judge monetary cases, but capital cases where there is an issue of לא תענה על ריב - לא תענה על רב, which forbids the other judges from disagreeing with the king, even kings of yehuda cannot judge.

The lechem mishna understands that the Rambam (Sanhedrin 2:4-5) disagrees with Tosafos. The Rambam holds that the drasha of לא תעשה על רב forbids a king from sitting on the sanhedrin, but doesn't disqualify him from judging privately. Therefore, a king of beis david can sit as a judge privately. To me it seems that the Rambam and Tosafos are both taking the same approach. Being that a king cannot be on the sanhedrin (even a sanhedrin of 23), he can never judge a capital case and will only be able to judge a monetary case.

There is a difficulty in the language of the Rambam. The Rambam in Hil. Sanhedrin (2:5) explains why a king of yisroel cannot judge:

לפי שאין נכנעים לדברי תורה שמא תבא מהן תקלה

The Rambam in Hil. Melachim (3:7) echoes this point:

מפני שלבן גס בהן ויבא מן הדבר תקלה והפסד על הדת

The Rambam provides a rational justification for a king being unfit to judge, and attributes it to their arrogance that will lead to a catastrophe similar to the story of Yanai. The Rambam is compelled to indicate that there is a difference between kings of beis david and kings of yisroel in their character, to explain why the concern of Yanai would be limited to kings of Yisroel.

The Kesef Mishneh seems to hold that the geziera was limited to kings of Yisroel because the Rabbonon were reluctant to make a decree forbidding kings of beis david from being judges, after the pasuk explicitly allows for it. But for kings of Yisroel where there is not explicit pasuk allowing for it, they were able to impose their gezeira (this is reminiscent of the taz y.d. 116 who says that the rabbonon don't make a gezeira that is against an explicit pasuk). But, the Rambam seems to make a very rationale distinction based on the different character traits of kings of beis david vs. kings of yisroel. In the commentary on the Mishna, the rambam is very clear about this character distinction:

זה במלכי ישראל בלבד, לפי שהיו עבריינין במלכותם לא היו משבחין השפלות, ולא היו נכנעין לדברי תורה. אבל מכלי בית דוד דנין ודנין אותם לפי שהם יודעים התורה ולא היה רע בעיניהם השפלות וההכנעה לדברי תורה לפי שמלכותם על פי התורה לא יגרע ממנו ענותנותם

The Rambam adds a line beyond the distinction in character. He explains why the tendency of kings of beis david is to be more humble. The malchus beis david is well deserved based on the Torah, therefore they don't need to enforce it with their arrogance. The Rambam gives a tremendous insight into human nature. When a person is confident about his status he doesn't need to enforce his kavod and is willing to be submissive to dinei torah. But, malchei yisroel who don't really deserve the status feel a need to enforce it, and therefore aren't willing to subjugate themselves to din torah.