Refusing to Vote on a Ruling to Which One Objects

[We continue, from last week, with an article that, one can say, deals with questions of democracy of a beit din panel. To what extent is one supposed to accept the decision of the majority and to what extent should one take unusual steps to try to force an outcome that he "knows" to be correct? Background to this section is that if one of the members of a panel says he does not know which side to the adjudication is correct, he is replaced by two others, who can arrive at a conclusion, and in theory could arrive at a different conclusion than the present majority (Sanhedrin 29a).]

The Shvut Yaakov (I, 138) was asked by a talmid chacham who was appointed to sit on a beit din with two ignorant men and saw that they are coming to an incorrect decision whether he could refuse to take a stand in order to force two dayanim to be added. He answered that although it would be lying to do so, since he has the noble intent of trying to prevent a travesty of justice, he may say he does not know. This is because one may distort a story in order to maintain peace.
In a similar case of three normal dayanim, the Beit Yaakov (15) says that one is not allowed to use such a trick. In citing the latter responsum and arguing, the Shut Yaakov says that a travesty of justice is a bigger problem than the value of the honor of the other dayanim. The Birkei Yosef (Choshen Mishpat 18:4) says that one cannot compare the different scenarios. The Beit Yaakov was talking about a case of a proper beit din, where one just strongly disagreed with the opinions of his colleagues. If one cannot convince the others of the superiority of his position, he cannot use a trick to prevent the ruling to be arrived at. However, the Shvut Yaakov discussed a case where the other two dayanim were ignorant people, in which case their ruling is not a legitimate one, and the Beit Yaakov would agree that one could say that he does not know. However, in the case of the legitimate beit din, the Birkei Yosef agreed that one could not take such a step. He implies, though, that the Shvut Yaakov would say even in that case that the lone legitimate dayan would be allowed to say he does know (the Urim V’tumim understood that way, as well). The Rav Pealim (III, 1) understood that the Shvut Yaakov would agree in the case of a legitimate beit din.
Rav Ovadya Yosef (Yabia Omer, CM 3) also understood that one should distinguish between the cases of legitimate and illegitimate dayanim. Thus, in the final analysis, in a normal beit din, a dayan must express his opinion accurately, even if, as a result, the other dayanim will overrule him.
[One would think that the explanation is that the single dayan may not reject the others as making an objective mistake. If so, if he has a way of "proving" to his friends that he is right but he knows that his proof is faulty, he should not falsely convince them, even if he thinks that his position is correct for a different reason.]