Following up on the clarification of the issue of “fixed status,”
in Ketubot 15:

“We follow the majority of the city only when there is also a majority of the caravan together with it; but we do not follow the majority of the city alone, nor the majority of the caravan alone. What is the reason? A decree was made regarding the majority of a caravan because of the majority of the city. And as for the majority of the city too—if they go to her, then whoever separated is presumed to have separated from the majority. It is only needed for the case where she went to them, for that is a fixed case. And Rabbi Zeira said: Anything fixed is treated as half-and-half.”

It seems that on the Torah level, “the majority of the caravan” is enough, since they are mobile.

And I didn’t understand. The problem with a “fixed” case, as I understand it, is that a prohibition that is fixed cannot be nullified (because of its importance), so how does it help me that the permitted side, which is the majority, is not fixed, while the prohibition—which is the minority that is supposed to be nullified—is still fixed in its place?

I don’t understand why the minority that is supposed to be nullified is fixed here. But I think that doesn’t matter, because I don’t think the law of fixed status is connected to importance.

You wrote:
“I don’t understand why the minority that is supposed to be nullified is fixed here.”

But it is explicit there: “It is only needed for the case where she went to them, for that is a fixed case.” The woman goes to the man who had relations with her, and he is fixed. Because of this we suspect that he is prohibited (that is, from among those who disqualify a woman from marrying into the priesthood).

In any case, what emerges from this is that a fixed prohibition is nullified by a majority of permitted things that are not fixed. And that is novel to me, however we explain the idea of fixed status. Isn’t it?

And what, in your opinion, is the explanation of “fixed status”?

I don’t understand. When the woman goes to the city, then both the majority and the minority are fixed. And when she goes to the caravan (and there is only a caravan—such as in a place of wagons), then both the minority and the majority are mobile.

“We follow the majority of the city only when there is also a majority of the caravan together with it”: the meaning is that she went to the man, and we do not know whether he was from the city (in which case he is fixed) or from the caravan.
In the case where there are simultaneously two majorities, we say: the majority of the city cannot save us, but the majority of the caravan can. And then we permit her.
That is, there is a fixed prohibition, and opposite it there are two majorities: one containing many permitted fixed cases, and one containing many permitted mobile cases, and we use them (the two majorities together—rabbinically) in order to permit the woman.
And the question is: how can a majority of mobile permitted cases nullify a fixed prohibition?

The prohibition is not fixed, but at most doubtfully fixed (perhaps she went to someone in the wagons of the caravan).
Let me remind you: your question dealt with a case of the majority of the caravan alone, but both there and here there is no fixed minority.
And let me also remind you that this whole discussion is based on your assumption that the law of fixed status is rooted in the importance of the fixed item, and in my opinion that is not so. Therefore, even if you were right that there is a fixed minority here, the discussion is not relevant.

You wrote: “The prohibition is not fixed, but at most doubtfully fixed.” That is not precise. There are variant readings and interpretations in the Talmud, but plainly according to Rashi there is a basic case in which it is known that “she went to them,” and because of that case they decreed also in other situations (where he went to her, or where it is not known who went to whom). In that basic case there is a fixed minority, because one of the townsmen is forbidden to the priesthood, and he is fixed in his house.

– The Sages were stringent in all the cases, and required “two majorities,” because two majorities would be effective even in the basic case (where there is “certainly fixed,” as above, and not “doubtfully fixed”); and because of that case they were stringent that there must always be “two majorities.”

I did not understand the rest of your remarks.

I am willing to give up the explanation I assumed regarding the law of fixed status. But I still ask for an explanation of the law and of the distinction:
Why, in the basic case (she went to him, certainly fixed), are two majorities effective? How can all the majorities in the world help nullify the fixed case?

I have now found in Shev Shma’tata (4:23) the following, and it seems he is asking my question:
“But what is difficult for me is this: since the main decree is because of a fixed case, and this is why we decree a case where they go to her because of a case where she goes to them, which is a fixed case—if so, what help is there in the majority of those passing through the city, since she had relations within the city? If she had gone to them, then even though the majority of those passing through the city are fit, since there is a minority of disqualified men fixed in the city, it is treated as half-and-half even against the majority of those passing through the city.”
The Shev Shma’tata goes on at length, and I haven’t yet had time to go through and understand it all, but it seems to me that he remains with this conclusion: that if we indeed know she went to him, then two majorities would not help.

I really do not understand. Indeed, the basic case is a situation in which there is a mobile caravan and a stationary city, and the woman went to the man who had relations with her. But still, the actual man she went to could be from the city or from the caravan, and therefore he is only doubtfully fixed. If the man was from the caravan, then even if the woman went to him, it is not fixed. Do you think that if the woman went to a man from the caravan, he is considered fixed because the woman went to him? Why assume that? The entire passage says the opposite.

I did not assume that if she went to a man from the caravan, his status is fixed. I assumed something else:

I assumed that if she went to him at home—“she went to him,” not “he went to her”—then certainly the man is from the city, because the caravan moves around in the streets and markets; only locals live in houses. So here there is “certainly fixed.”

And I understood that because of this severe basic case, they were stringent that there must always be two majorities, because two majorities would help even in such an extreme case.

Do you understand it differently?

Obviously differently. She went to the man, but it is not known whether the man was from the city (and she went to his house) or from the caravan (and then she went to his wagon).

If it is clear that she had relations with a resident of the city, then the fact that there is a caravan there changes nothing. We consider only the group of city residents.

See column 237, which was posted בעקבות the thread here.