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The Chida (Shem Hagedolim 10) cites a machloket among Rishonim about what to do when a much more knowledgeable dayan finds himself in the minority against two low-level dayanim. The Ra’avad says we follow the majority. He bases himself on the gemara (Yevamot 14a) that says that Beit Shamai were sharper than Beit Hillel and yet we accept the opinions of Beit Hillel, who constituted the majority. The Hagahot Oshri concurs.
The Sha’ar Ephrayim (10) cites Rav Hai Gaon who argues and says as follows: "If they are equal in wisdom, we leave the words of the individual and follow the words of the majority, and if the one is greater than the two, we follow the one who gives good reasoning for his words." The Ramban (Sanhedrin 32a) argues with Rav Hai Gaon. It seems that the disagreement is whether that which we follow the majority is a set concept of following a majority or whether we are to follow a "majority of wisdom," just that we assume until we know otherwise that the majority of people contains the majority of wisdom.
The Sefer Hachinuch (#78) says that the matter depends on the context of the machloket. In general, that which we follow the majority even when their ruling is considered of lesser quality is true only in a formal setting, such as Sanhedrin [or beit din]. What is special there is that there is a need for a set number of people and that the Torah explicitly commands us to follow the majority no matter what. The Minchat Chinuch (ad loc.) says that this is explicit in the fact that Beit Shamai did not have to rescind their rulings despite being the minority, as their acumen was important because their machlokot with Beit Hillel were outside the formal setting of Sanhedrin. The Hagahot Oshri says that even in regard to a machloket outside of beit din, we follow the greater in number, and even Beit Shamai stopped relying on their opinions after the Heavenly voice sided with Beit Hillel. The S’ma (25:18) understands the Rama as following the less compelling majority even for machlokot outside beit din.
The Shvut Yaakov (I, 137), related to being outnumbered by two ignorant "dayanim" and said that the majority wins, as long as there is one learned dayan, even if he is the minority dayan, to validate the beit din. The Sha’ar Mishpat (18:1) disagrees since, if the beit din is valid only due to the minority dayan’s expertise, how can they rule against him? He says that even the Ramban accepted the majority only when they were valid dayanim, just that the minority was exceptionally qualified.
In any case, most Rishonim and Acharonim indicate that, within beit din, we follow the majority even if they do not compare in wisdom to the minority opinion.
P'ninat Mishpat (829)
Various Rabbis
159 - Paying for Construction Work That Was Destroyed by the Authorities
160 - Following the Majority When the Minority Is More Knowledgeable
161 - Compensation for Withheld Salary
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P'ninat Mishpat P'ninat Mishpat: Multiple Agreements and Parties – part IV
based on final ruling of 80082 of the Eretz Hemdah-Gazit Rabbinical Courts
P'ninat Mishpat P'ninat Mishpat: Sharing in Plumbing Expenses – part I
based on ruling 85013 of the Eretz Hemdah-Gazit Rabbinical Courts
P'ninat Mishpat P'NINAT MISHPAT: A Mess of Loans, Repayments and Grievances – part II
based on ruling 83033 of the Eretz Hemdah-Gazit Rabbinical Courts
P'ninat Mishpat P'ninat Mishpat: Undoing a Problematic Partnership – part III
based on ruling 84061 of the Eretz Hemdah-Gazit Rabbinical Courts
Rabbis in Midrash
Lessons
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Kuzari -Rabbi Ari Shvat Kuzari class 9 - "Seeing is Believing" (parag. 21-30)
These paragraphs elaborate on the theme that seeing and knowing is better than any attempt to prove logically, and begins explaining the difference between Israel and gentiles.
Ein Aya Various Universal Stages of the Geula Process
Rav Kook examines the various stages of redemption, explaining how (in addition to the obvious oft-mentioned stages of ingathering the exiles, reviving the Hebrew language, army, state etc.) the messianic dream of world prosperity, the State of Israel and world unity can and are realistically and logically gradually coming true.
Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
How do we know that the "claim" of mass revelation to 2,000,000 witnesses at Mt. Sinai is really true? This important class answers all of the questions skeptics ask about this claim of the Kuzari.
Ein Aya Armies Still Necessary for Balance & the War Against Wars
Rav Kook explains why the world was originally divided into the various seemingly contradicting ideologies and cultures, in order to develop each one respectively. Swords or armies symbolize how each respective ideology defends themselves, as well as deters their opposing ideologies and cultures. On the other hand, the messianic era will be one of peace, and Rav Kook explains the transition to that stage, which mankind is already undergoing.
The Land of Israel LGBT'S IN ISRAEL
The question was asked, how can one make Aliyah with the LGBT parades?
Kuzari -Rabbi Ari Shvat Kuzari class 7 - Five Accumulative Proofs of G-d
As a preparation for the Kuzari's classic proof of G-d from the mass-revelation at Sinai, we start here with 5 other directions to strengthen our belief which also contribute to what the Kuzari will present as well.
Ein Aya Muscle & Meaning: The Dual Nature of Gevurah (Physical Strength)
Is physical strength and fitness a necessity or an ideal? Although it if often totally overlooked among topics of Judaism, Rav Kook writes that it clearly is also a necessity to deter the many enemies of Israel, but even in Y'mot HaMashiach, in the Messianic era, to a certain extent, it's ideal continues even after our enemies will have been finished off.
