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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 (832)
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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