(a) It is said that Bais Shamai was "chaddadim" --sharper than Beis Hillel.
Is there a way of seeing this from their opinions? ie can you give some
examples of how they were sharper? or is there a different definition of
"chadadim" with a more subtle meaning. If a person goes to 100 doctors and
99 gives one opinion and the one who is the most expert in the particular
problem gives another--whose opinion should one follow?
(b) In getting at psak if rabbi a & b have one shita and rabbi c has another--a
& b might not be a majority if b is a student of a. He is just repeating
his rebbi's psak...so if the students of bais Hillel were more numerous-- it
doesn't mean that they were in the majority if they were just repeating
their rebbi's psak. If the above is true, what is the meaning of majority?
(a) You are asking a good question, but it is not within our abilities to judge what makes a person (or school) greater in wisdom than another. Also, Halachic P'sak is not always dependant upon who is sharper, as we find sometimes that the Halachah is not like a certain opinion because "he is too sharp" ("Mechudad T'fei"), and "his colleagues did not fathom his intentions" ("Lo Amdu Chaverav Al Sof Da'ato") in Eruvin 13b.
The Torah tells us that "Rov," the majority opinion, is the one which we follow.
(b) "Rov," the majority, refers to the majority of the greatest Sages of that generation. Who their teachers were is not relevant. The fact that the majority of the greatest Sages of the generation chose to join the academy of Hilel is indicative.