The Gemora says that we follow Beis Shamai by the 18 cases because they were the majority.
My question is if so why do we ever follow Beis Hillel ? Did Beis Shamai suddenly become the minority ? Furthermore the Gemora states elsewhere (Eiruvin) that we follow Beis Hillel,because a Bas Kol rang out from heaven to follow them. Isn't that enough off a reason to follow Beis Hillel even by these 18 cases ?
Tzvi, Chicago
Beis Hillel was the larger group and usually the majority.
The 18 cases in the Mishnah 13b were decided in the Aliyah of Chananyah, where, unusually, Beis Shammai was the majority, only at that meeting.
As far as a Bas Kol: you quote Eruvin, but see there that there is an opinion that "Ein Mashgichin b'Bas Kol." Also, Tosfos in Bava Metzia 59b explain that a Bas Kol can back up only the majority of Beis Hillel to "win" (even though Beis Shamai was sharper), but you cannot use Bas Kol against a Rov (such as to go with Rebbi Eliezer there), so here, too, a Bas Kol cannot eliminate the view of the majority, Beis Shamai, in these 18 cases.
All the best,
Reuven Weiner