Tradition has it that a bat kol declared that we follow Beit Hillel’s rulings over those of Beit Shammai.
Tosafot (Eruvin 6b) note that more people belonged to Beit Hillel than Beit Shammai and therefore the halacha should have followed Beit Hillel based on the rule that we follow the majority opinion (“acharei rabim l’hatot”). What, then, was the purpose of the bat kol? Tosafot suggest that the bat kol taught that the halacha follows Beit Hillel despite the fact that Beit Shammai was sharper and more intellectually agile than Beit Hillel.
Not only does the halacha not follow Beit Shammai, but it seems that ruling like Beit Shammai is actually assur. Berachot 10b states that Rav Tarfon even deserved to be punished for ruling like Beit Shammai.
This Gemara seems strange, though. To apply its reasoning to modern times: The majority of poskim often disagree with the rulings of the Vilna Goan or Rabbi Akiva Eiger, for example, but no one would ever say that a posek deserves to be punished for ruling like these two great rabbinic figures.
The Chatan Sofer (Chatan Torah, P’ticha l’shitat Rov, p.2) notes that majority opinions are not necessarily correct. Indeed, a minority opinion can be more logical and sharper than a majority opinion. Yet, the bat kol in the case of Beit Hillel and Beit Shammai declared that the halacha follows Beit Hillel irregardless and the opinion of Beit Shammai is considered meaningless – “k’man deleisa.” Does that mean that the minority opinions of the Vilna Gaon are also “meaningless”?
One theory (Get Pashut, Kuntras Haklalim 20) maintains that the rule that we follow the majority opinion – even when the minority opinion is offered by a sharper mind – only applies to cases where the two parties talk to one another and hear each other’s arguments. When both opinions, however, are just found in books, one need not follow the majority opinion since the party with the majority opinion might have changed its ruling had it heard the other side’s reasoning.