bitul b'rov and rubo k'kulo

We have on the one hand a principle of “rubo k’kulo” that tells us that 51% of something is the same as 100%.  For example, cutting 51% of the simanim of an animal is a kosher shechita – you don’t need to cut 100% of the way through.  We have on the other hand a principle of bitul b’rov that tells us that a lesser quantity can be ignored when mixed in with a larger quantity.  Both of these rules are learned out from “acharei rabim l’hatos,” the pasuk that tells us to follow the majority vote in any case that comes before beis din.  But how can that be?  Let’s say two dayanim vote chayav and one dayan votes patur: if we use the principle of rubo k’kulo, the majority vote counts as the decision of the entire court – there is no miyut that needs bitul.  If we say that the one vote of patur is bateil and therefore doesn’t exist, we don’t need to come on to rubo k’kulo – all the votes are accounted for.  How do we learn both principles from the same pasuk – it seems it’s a choice of either/or?

R’ Mordechai Greenberg, R”Y of KBY, uses (link) the Oneg Y”T from yesterday’s post to resolve this question.  The Oneg Y”T writes that bitul can only be used to negate a quality, but not to assign some new quality to an object.  A piece of treif meat can lose its status of issur through bitul, but tzitzis not spun lishma cannot be treated as if they were made lishma through bitul.  R’ Chaim Brisker (stencil) explains that beis din has two functions: 1) to determine truth and 2) to rule based on that determination.  If we didn’t have a din of rov, then anytime there was disagreement among the dayanim we would have to assume 1) they could not discover the truth and 2) a divided court could issue no verdict.  We need bitul b’rov to allow us to ignore the vote of the dissenting dayanim and say that the truth is with the majority.  However, based on the Oneg Y”T’s principle, bitul cannot convert dissenting votes into votes of agreement.  Beis din may know the truth, but two dayanim cannot issue a verdict without a third partner to complete the court.  It's the din of rubo k’kulo that transforms  the majority vote into what effectively is considered a ruling of the entire court.