After many to tilt – democracy

Hello Rabbi!
I just watched the lesson on YouTube about “A Philosophical View of the Controversy”
The Rabbi says there that the majority always needs the consent of the majority, the consent given when both entered the game…..
Is it like that in the Sanhedrin, where the majority is to be swayed? Or does the Torah say that the correct logic is to follow the majority? And if that’s the case, perhaps here too, even if the minority does not agree to follow the majority in its opinions, because they do not agree with the rules of the game, the minority will be forced to follow the majority…
Despite my words, the logical connection between Beit Shammai and Hillel will remain problematic.
 
Thank you very much!