When I write “a plausible majority,” I mean that it does not seem plausible to me that in a case where there is obvious cooking going on (like in the example with the sauce), we should follow the solid majority. Because following the majority in such a case does not seem plausible to me… The wording really was not good. But I explained what I meant.

Dvir, I vaguely and dimly remember that Rabbi Shalom Messas disagreed with Rabbi Ovadia, and from what I remember his main claim and astonishment was like yours: that it is not plausible to fully cook the sauce just because there is a lot of chicken next to it in the pot. And Rabbi Ovadia (according to the hazy memory above) dismissed it with “that’s just how it is.”

[By the way, there is a Talmudic passage where nullification by majority is not relevant for impurity by carrying (regarding kosher ash that became mixed with ash from a furnace, where even if most of it is furnace ash, if one carries all of it he becomes impure through carrying), unlike touch, where one touches just one part. And there there is a big tangle among the commentators. At first glance, cooking is similar to carrying and not to touch. One would have to study Rabbi Ovadia’s responsum and see what happens there].

You are simply repeating the same question again, and I already answered it. You could say the exact same thing about any nullification by majority. You ate a dish in which there is a non-kosher minority, so you definitely ate non-kosher food—so why should I care that there is a kosher majority there?

I am not familiar with Rabbi Ovadia’s statement, but in my opinion this is not about nullification by majority but about the rule that “its majority is as the whole of it” (although some understood these as laws stemming from the same root). Simply put, its meaning is that the essence of a thing is determined by its majority. For example, if most of Israel is impure and some are pure, then we do not postpone to the second Passover; rather, they bring the first Passover in impurity. Note that here there is no nullification by majority (there is no mixture at all, and it is known of each person whether he is impure or pure); rather, this is a rule that “its majority is as the whole of it.” The nature of the group is determined by the character of its majority. You have to decide whether the people of Israel (the public) are impure or pure. Since some are one way and some the other, the status of the public is determined by the status of its majority. [As stated, some explained nullification by majority this way as well.]
And for our case: if there is mostly cooked food there and only a minority of sauce, then when I ask you what you placed on the hotplate, you will say: I placed cooked food on it. If there is mostly sauce, then you cannot say that you placed cooked food there, and therefore it is forbidden. Very simple.
If you squeeze a lemon on the Sabbath into a salad or onto sugar, then you did not squeeze. Why not? Because the lemon gets mixed into the food, and now we do not have a liquid but a solid. Squeezing is extracting liquid from a solid. Does that sound more logical to you? And that is straight from the Talmudic law.

Besides, the sauce was in fact already cooked. This is only a stringency, as though there is cooking after cooking for liquids [with sauce it is even stranger].
And besides, on the Sabbath what matters is not the scientific facts of whether you cooked or not [and factually, the sauce certainly already went through its cooking, and now this is only reheating], but rather what people would call what you did; the Torah prohibited only intentional, constructive labor. And if in people’s minds you heated chicken [and with dry food everyone agrees there is no cooking after cooking] with sauce [certainly when it is the minority], then it is chicken with sauce—the story here is the chicken, and you only heated, not cooked; and you only heated chicken, not liquid, but chicken with what is secondary to it.