The first mishna in Succah says that if there is more sun than shade, the succah is פסול.
Rashi writes:
"המועט בטל ברוב והרי הוא כמי שאינו ועל שם הסכך קרוי סוכה".
The smaller area where there is shade is nullified ["ביטול"] by the larger area where there is sun and it is like it doesn't exist. And he strangely concludes with a non-sequitur: The succah is called thus because of the סכך.
Asked the Chochmas Shlomo: What does Rashi mean?? The rules of ביטול don't apply when the מיעוט [minority] is clearly recognizable, as it is in our case where the shade is clearly recognizable. Also, in the opposite case where there is more shade than sun, we wouldn't be able to apply the rule of ביטול because the sunny, non-covered part is clearly recognizable.
He answers that we only say that there is no ביטול if it is a דבר הניכר, when we come to eat or otherwise use the מיעוט itself. But here regarding succah, since we are not using the מיעוט itself independently [the area where there is no סכך] but rather the ENTIRE area under the סכך, we can say that the name and status of the the entire area is determined by the majority. That is why Rashi concludes "על שם הסכך קרוי סוכה" - The kashrus of the succah is determined by the סכך, and thus we can apply the rule of ביטול ברוב if it is mostly סכך.
The Steipler ['קה"י סי' א] and Rav Shmuel Rozovsky [ספר זכרון שמואל] explain differently: Rashi is not referring to the rule of ביטול ברוב, that applies, for example, when a piece of meat falls into a pot filled with dairy where if there is 60 times the meat, it is nullified. He is rather referring to the rule of "רובו ככולו" which applies, for example, when one drinks MOST of the wine in his kiddush cup, we view the whole cup as being drunk. Because we view the whole cup in its totality - was it drunk or not? If most was - then we view it ALL as being drunk. So too, the question is if this succah is considered "shady". If most of it is then we view it as being shady in its entirety - רובו ככולו. Most makes whole. It can thus be deemed a "shady succah" [no relation to "shady character" or "shady business deal". Or "he is going out with Shaindy". That is "Shaindy" and not "shady"].
After bowing down to and kissing the feet of the aforementioned GREAT Geonim, it is very hard to read their explanation in Rashi. Why did he say "בטל ברוב" if he meant "רובו ככולו"? Also, Rashi says that the מיעוט is if it doesn't exist. That sounds a LOT more like ביטול ברוב than רובו ככולו.
There is a TREMENDOUS AMOUNT of literature about this. HaGaon R' Baruch Mordechai Ezrachi [who couldn't accept the aforementioned explanation because of the questions raised] explained Rashi to mean that the succah MUST have סכך in order for it to be defined as a succah [as Rashi says explicitly that it is called סוכה because it has סכך] explained [if I understood correctly] like the Chochmas Shlomo before him [although he doesn't mention him]:. If there is mostly shade then the area is defined as a succah. If not - it is not. When Rashi talks about ביטול ברוב he is not referring to ביטול ברוב in the יורה דעה sense but rather means that if there is mostly sun, the shady part is "halachically insignificant" [that is the ביטול] because the רוב sun, creates a non-succah area. It is thus "כמי שאינו" - it is like there is no shade at all because the סכך only creates a kosher succha when there is רוב shade. [This, incidentally, has no connection to demons]. See Birkas Mordechai [Sukkos 18] for a detailed and expanded explanation.
