a taxonomy of rov: acharei rabim, bitul b'rov, rubo k'kulo

Judging from comments to the previous post, the audience is getting restless because of lomdus deprivation. More on Nisan-Iyar maybe later, but first a R’ Chaim to satisfy the lomdus craving. Those learning daf yomi recently came across the source for the din of rubo k’kulo (Nazir 42a). The Torah tells us that a nazir must cut all of his hair, not just a majority of his hair. The implication is that if not for the special gezeiras hakasuv in this case, cutting rov would suffice as if all the hair was cut. The Maharat”z Chiyus notes that although the principle of rov is well established elsewhere as a din d’oraysa (Chulin 11), there is an added element of chiddush to the din of rubo k’kulo. Had we only had the principle of rov, we would know that a majority counts as more than a minority, but the minority would still be theoretically present. Rubo k’kulo goes a step further and teaches that we treat the minority remnant as non-existent. For example: on Pesach night where according to some Rishonim one must drink the entire kos of wine, drinking the majority of the kos is considered equivalent to drinking the entire cup.

A full taxonomy of the concept of rov should include two other halachos, both learned from the pasuk of “acharei rabim l’hatos”: 1) the principle of following a majority; 2) the principle of bitul b’rov. Again, these are two very different chiddushim. The basic principle of following rov is useful to solve a safeik, e.g. if there are 9 frogs and 1 sheretz near a loaf of terumah and one of the above came in contact with the terumah, rov allows us to say with a degree of certainty that it was a frog and not a sheretz. Bitul b’rov is a different concept entirely. If a drop of milk fell into a pot of meat, bitul b’rov tells us that if the pot contains enough meat, it can be eaten. In the former case, rov tells us that a sheretz did not come in contact with the terumah. In the latter case, the halacha of bitul tells us that even though the milk fell into the pot, the meat can still be eaten.

R’ Chaim Brisker asked how these two very different halachos can be derived from the same pasuk. In a nutshell, R’ Chaim’s answer is as follows: “acharei rabim l’hatos” tells us that the psak of beis din always follows the majority. Tosfos (Bava Kamma 27) asks how we can decide dinei mamonos based on rov dayanim when we know that the principle of rov is not applicable to dinei mamonos. R’ Chaim explains that once beis din arrives at a psak, their conclusion is not just considered the conclusion of a majority of the judges, but is considered the conclusion of the court as a whole. The conclusion may be arrived at by polling the majority, but once decided, the minority of dayanim are bateil b’rov. Both halachos, rov and bitul b’rov, are operative in the psak of beis din.

Here is a question that has me stumped, and I am sure I must be missing something. Couldn’t the operation of beis din in cases of dinei mamonos be explained based on the principle of rubo k’kulo and not based on bitul b’rov? In other words, if 2/3 of the court reaches consensus, rubo k’kulo would mean that it is as if the entire court has reached a consensus. The justification for psak in dinei mamonos would therefore stem from the gezeiras hakasuv in hilchos nezirus, not from "acharei rabim l’hatos". If the operation of beis din could be explained in this way, then R' Chaim's question is left hanging: what is the source for the halacha of bitul b’rov in scenarios like a drop of milk falling into the pot of meat?