Is there any gaon or medieval authority who holds that a person can make a halakhic decision against the view of the rabbis if he himself is not qualified in such matters?

An amusing question. What does “the view of the rabbis” mean? Which rabbis?

For example, regarding the question itself, it seems to me that the overwhelming majority of rabbis today, and perhaps throughout the generations, hold that an ordinary person cannot clarify a halakhic topic for himself if he is not qualified to issue rulings. So I asked the Rabbi whether he could point to sources that say the opposite.

That is not what you asked. But for our purposes, I did not write that he can clarify a halakhic topic for himself if he is not qualified in such matters. On the contrary, I have written several times in the past that only someone qualified in such matters can issue a ruling for himself. But when he comes to choose the position of one rabbi or another, he can do that himself, and he is not obligated to stick to one rabbi.

Thank you for the clarification, Rabbi. Could I please ask for some source from the Geonim or the medieval authorities that says this?

That is, that an ordinary person can choose the position of a certain rabbi from across the generations on a given topic.

Here I saw a summary of the topic:
http://www.halachabrura.org/dafyomi/eruvin2.htm

But how can one infer that this is talking about an ordinary person? הרי they are discussing deciding between the views of halakhic decisors, and for that one needs to be qualified in such matters, as you wrote in your article on autonomy in Jewish law, no?

Why assume that? If you are yourself a halakhic decisor, you do not need to decide anything at all; you simply do what you think.

That is how I understood it from sources in the Rabbi’s article and elsewhere:

Geonim: “You asked: where there are two responsa from two Geonim who disagree with one another, and each of the litigants or judges has adopted one of them, what do we do?

Answer: The judge who is the greater one according to the times and in understanding should decide in favor of whichever one seems right in his eyes. And what he decides in his heart stands; if one litigant relies on the words of the other Gaon, we do not heed him…”

Rosh: “And where two great authorities disagree in a halakhic ruling, the judge should not say, ‘I will rule as whichever one I want,’ and if he does so this is a false judgment. Rather, if he is a great scholar, learned and understanding, and knows how to decide in favor of one view with clear and convincing proofs, he has permission to do so. And even if another scholar ruled differently in another matter, the scholar may refute his words with proofs and disagree with him, as I wrote above—certainly if he has support from one of the disputants. But if he is not qualified in such matters, he should not extract money in a case of doubt…”

A quote from the Rabbi’s article: “From the wording of the Rosh it appears that even regarding deciding unresolved disputes, the scholar must be ‘qualified in such matters,’ since the Rosh concludes the above passage with the words: ‘And if he is not qualified in such matters, he should not extract money in a case of doubt,’ which implies that even deciding an unresolved dispute among the halakhic authorities cannot be done by someone who is not ‘qualified in such matters.’”

The Rema (Choshen Mishpat 25:2): “A person should not say, ‘I will rule as whichever one I want,’ in a matter where there is a dispute… Rather, if he is a great scholar and knows how to decide with proofs, he has permission to do so, and if he is not qualified in such matters… if it is in the area of prohibitions and permissions, and it is a Torah-level prohibition, he should go stringently, and if it is a rabbinic matter, he should follow the lenient view.”

If possible, could I also ask what the Rabbi’s definition of someone “qualified in such matters” is?

They are speaking about judges, not halakhic decisors. There is a very large difference. A judge decides, and his decision is binding. Moreover, a judge is not supposed to decide according to his personal reasoning, since there is an issue of certainty and uniformity in law. Therefore, from the standpoint of a judge, he decides between existing opinions. A halakhic decisor, by contrast, rules according to what appears correct to him. He is not supposed to be troubled by the existence of different views, unless he himself has no position of his own. A layman cannot decide in Jewish law either, but he can rely on a halakhic decisor who seems right to him, since that decisor is qualified in such matters. The Rema of course does not hold like me, and I wrote that in the article. He belongs to the precedent-based approach, and the entire article is devoted to presenting a different position.
There too I briefly addressed the question of who counts as qualified in such matters.

“A layman cannot decide in Jewish law either, but he can rely on a halakhic decisor who seems right to him, since that decisor is qualified in such matters.”

Could I please, please get some source that says this?

That a layman can rely on different halakhic decisors from different generations on different topics, as seems right to him.

I’ve exhausted this.

Did I ask for something illegitimate?

The honored Rabbi is saying something that seems to me to contradict the position of all the halakhic decisors in our generation and before it, all the way back to the Talmud, from what I have encountered until now. Is it not legitimate to ask the Rabbi for a source for his statement?

Or suppose this is an innovative argument of the Rabbi’s—perhaps to give some Talmudic source that would indicate that it is correct.

Everything is legitimate, and by the same token it is legitimate from my point of view to say that it is neither interesting nor important. If I advocate autonomy, it seems strange to me to demand precedents for the claim that one need not rely on precedents. I explained that in my view this is what is written in the Talmudic passage itself, and that is enough.