Our Gemara on Amud Aleph discusses the well known Talmudic principle Of רובו ככולו the majority is considered as if it is the complete whole. There are numerous halakhic applications of this principle such as slaughtering most of the animal’s windpipe and foodpipe counts as it being fully cut, or closing most of a walled area as if it is fully closed.
The Chasam Sofer (OC #140) discusses a famous question: If we say that the majority counts as the whole, why do we not apply that to shiurim? If you have more than a half of a kzayis of matzah, let us say it’s as if you ate a full kzayis! The Chasam Sofer answers with a fundamental distinction. In the Torah we follow the majority, in the sense that you have an entire amount present, and the majority converts the minority over, and the minority now is not considered separate from the whole. Thus, if the majority of judges rule one way, the entire court now is considered as ratifying and confirming the ruling. Or if one non-nkosher item gets mixed up with two indistinguishably kosher items (for example, one non-kosher slice of salami with two kosher ones), the entirety is considered kosher. The majority overtakes the minority, and it is seen as one unit.
However, when it comes to shiurim, the Torah requires an amount. ¾ of a kzayis is not the requisite amount. The majority can convert the minority but it cannot CREATE the majority.
The Chasam Sofer illustrates this with an illuminating example from the laws of minyan. While we require ten for a minyan, for certain prayers we require that a demonstrable majority did not pray yet. So seven out of ten who did not yet pray is fine. However, we still require seven OUT OF ten, and you can’t just have seven people and say that’s a minyan.
Metaphysically, what does this mean? The presence and involvement of people is a requirement, even if their opinion is not followed. The process requires counting them and involving them, even when their view is the opposite. The Jewish Beis Din has a minimum number of judges for various rulings. For example, we require 23 judges to administer capital punishment. When the majority rule is pronouncing him guilty, the entire court is enacting it, not just the majority. This is similar to the idea that we study the views in halakha even when we do not rule in accordance with that view. Much of Yevamos deals with complex scenarios that arise from the opinion of Beis Shammai. The ethical idea is that cooperation is not about the minority disappearing but rather about it being present and counted, and becoming part of the majority.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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