To compel means beating him until his soul departs. If there is doubt whether he may already have fulfilled the commandment, does it make sense to you that there would be permission to hit him?

If you meant coercion without violating a prohibition, one could perhaps say that it depends on the dispute between Ketzot and Netivot whether coercion is by way of punishment and can be carried out only by a religious court, or by way of mutual responsibility and can be carried out by any person.

Definitely. Why not? As I explained, if there is an obligation to be stringent and do it, how is this different from any other halakhic obligation over which we compel?
So I also do not see any connection to the dispute between Ketzot and Netivot.

Can Reuven, who is obligated in Grace after Meals only because of doubt, discharge Shimon, who is definitely obligated (or obligated because of doubt)? That is, does each person evaluate the doubt independently, so that Shimon rules stringently that Reuven is exempt, or is the root of the doubt determined where it arose, and in the end Reuven is obligated? Simply speaking, the religious court is like Shimon, and there is a view among the later authorities that he does not fulfill his obligation, and therefore similarly the religious court does not compel. But perhaps coercion really is a special matter judged according to the person as he stands, and therefore perhaps the religious court compels even if Shimon would not fulfill his obligation.
I once saw this topic in a responsum of Rabbi Ovadia regarding the blessing over eruv tavshilin at twilight (when there is doubt whether the holiday has already begun, but the Sages permitted making the eruv then), and if I remember correctly he rules that one does recite the blessing. And if so, plainly the same would apply that the religious court compels. But I do not have the book in front of me right now.

The responsum is in Yechaveh Da'at 6:31. The full file is here https://tinyurl.com/v6bdc27c.

"If someone forgot to make an eruv tavshilin on the eve of a holiday, and remembered after sunset, can he still make an eruv tavshilin with a blessing? … However, one must consider the blessing over the eruv: should we say that since twilight is doubtfully day and doubtfully night, he should not recite a blessing, because in cases of doubtful blessings we are lenient? Or perhaps we should say that since in any case the Sages permitted making an eruv tavshilin during twilight, and one may rely on it to cook from the holiday for the Sabbath, one must recite a blessing over it."

"And the proof for this is from Tosafot on Menachot (page 66), s.v. 'it is a memorial to the Temple,' that at doubtful nightfall one may recite a blessing and count the Omer, and need not wait until it is certainly night, since counting the Omer nowadays is only rabbinic, and with a rabbinic doubt we are lenient… Thus we learn that with a rabbinic commandment that was permitted to be performed during twilight on the basis of leniency in rabbinic doubt, the doubt is treated as certainty, and one may recite a blessing over it. And the same applies in our case: since it was permitted to make an eruv tavshilin during twilight, one should recite a blessing over the eruv in accordance with the enactment of the Sages."
He also cites Sha'arei Yosher 1:8, that according to the view that doubt is treated stringently on the Torah level, it becomes like certainty.

As for whether one who is obligated in Grace after Meals because of doubt can discharge someone definitely obligated, there is a dispute among the later authorities there, between Pri Chadash (he can discharge) and Rabbi Akiva Eiger (he cannot). It seems the difference is that a blessing branches out from the obligation of the commandment itself (like the well-known view of Radbaz that if the doubt is in the commandment, then one does recite the blessing. For some reason that was not brought in Yechaveh Da'at there), and that is not similar to discharging someone else, where according to Rabbi Akiva Eiger, one who is obligated because of doubt does not discharge one definitely obligated. According to this, it would seem more likely that coercion by the religious court also branches out from the obligation of the person in question and is similar to a blessing, not to discharging another's obligation.

It seems very implausible to me that someone obligated because of doubt could discharge someone definitely obligated. On the possibility that he is not obligated, what he is now fulfilling is only the laws of doubt, and one can say that his blessing is not in vain. But he is not fulfilling the commandment of Grace after Meals.
As for someone obligated because of doubt discharging another person also obligated because of doubt, that can be discussed (although logically, in my opinion, even there he does not discharge him).
But in any case I do not see any connection to the questions of coercion.

Rabbi Michi,
If we adopt Rabbi Akiva Eiger's view that someone definitely obligated in Grace after Meals remains in doubt even after hearing it from someone obligated only because of doubt,
and we adopt Tosafot in Menachot that someone counting the Omer at doubtful nightfall may also recite a blessing over it, and Yechaveh Da'at that one who makes an eruv tavshilin during twilight recites a blessing,
and Radbaz that if the doubt is in the commandment then one recites a blessing (if there is doubt whether he took the lulav, he takes it and recites the blessing),

then is coercion by the religious court more similar to the blessing over commandments, and therefore the court compels, or to discharging another's obligation, and therefore the court does not compel?

I commented before seeing your response. Now I do.

Why is there no connection to the question of coercion? To my mind it is all one issue: whether each person evaluates doubts for himself, or whether the root of the doubt decides and becomes like certainty because right now an ordinary obligation rests on him.
If the definitely obligated person can indeed fulfill his obligation through the one obligated because of doubt, then clearly it would seem that the religious court compels. If the definitely obligated person cannot fulfill his obligation through the doubtful one (Rabbi Akiva Eiger), and yet with blessings over commandments the blessing follows the doubt in the commandment (and that is judged leniently, such as counting the Omer at doubtful nightfall or making an eruv tavshilin during twilight, and therefore one also recites a blessing over it), then it remains to be clarified whether coercion is similar to discharging another's obligation or to blessings over commandments.

Just as witnesses validated by majority rule (two witnesses came out from a group of one hundred Jews and one non-Jew) are effective even to extract money from someone in possession, though for that majority ordinarily does not help.

The statement that he is not fulfilling the commandment of Grace after Meals is not clear to me. So what commandment is he fulfilling? If someone eats non-kosher fat based on the testimony of one witness, did he violate the prohibition "listen to one witness in matters of prohibition," or did he violate the prohibition "do not eat forbidden fat"? There is no such prohibition as listening to one witness in matters of prohibition (Rabbi Shimon Shkop proves from this that if it turns out in the end to have been permitted fat, he is not flogged), and there is also no commandment to recite a blessing because of doubt. The only commandment that exists is the commandment of Grace after Meals. They discuss whether a half-measure in a prohibition punishable by karet is more severe than a half-measure in a regular prohibition, or whether all half-measures are one separate prohibition in itself.

Rabbi Shimon Shkop there discusses exactly these two possibilities in understanding the laws of doubt: whether this is a prohibition against entering a state of doubt, or a concern for the original prohibition itself. The same applies to doubt regarding a positive commandment (according to the side that one must be stringent in a doubtful positive commandment). Thus the obligation to recite Grace after Meals because of doubt may be interpreted as an obligation to leave the state of doubt, or as an obligation to recite Grace after Meals.
In any case, I simply cannot understand the connection between coercion and discharging another's obligation. What does one have to do with the other?

The religious court and discharging another's obligation depend on the same question: do they evaluate the doubt for themselves stringently, so that the other person is *not* obligated, or do they evaluate it from the other person's perspective, and then see that an obligation definitely rests on him because of the doubt?

What do you mean there is no connection? How could it be that the other person fulfills his obligation by hearing from someone obligated because of doubt, but the religious court would not compel?

I really do not grasp the connection you are making here. You keep repeating it again and again, and I do not have the slightest understanding of what you mean. I am not even disagreeing. I just do not understand.
The religious court compels a person to do his duty. If So-and-so has a duty to be stringent when he is in doubt, then that is a duty like any other, and therefore they compel. And even if according to the law a doubtful obligor does not discharge someone else who is definitely obligated, that is only because of the possibility that in truth he may not be obligated. So this has no connection whatsoever to the question whether they compel him to fulfill his duty to be stringent in a case of doubt.

If it is a duty like any other duty, then why can he not discharge others in Grace after Meals?

I explained. It is a duty to be stringent in cases of doubt (to leave the state of doubt), not a duty to recite Grace after Meals. A borrowed analogy: do we compel regarding a half-measure? Apparently yes (in practice it is a Torah prohibition). But the later authorities already pointed out that this is not necessarily the same prohibition as the prohibition in the full measure.

And according to the side that he does discharge another's obligation (Pri Chadash), is it possible that the religious court still would not compel?
I mentioned above the question whether a half-measure of a karet prohibition is more severe than a half-measure of a regular prohibition. I think the assumption is indeed that it is more severe.

In my opinion, yes. He discharges the obligation, since at the end of the day he is reciting Grace after Meals. But still, if there is a chance that he is not obligated, and he has already recited it and wants to take the risk, it is possible that the religious court would not compel him.

What is the side that the religious court would not compel?
I understand that the side is as follows: the religious court evaluates the doubt for itself stringently, that it is forbidden for them to compel him (a doubtful prohibition), while he evaluates the doubt for himself stringently (a doubtful positive commandment), that he is obligated to fulfill it.

That is really not necessary. The religious court works out his account, and sees no justification to compel him if he decides to take a risk. We compel only where it is clear that there is a transgression. As I wrote, if the very obligation to be stringent makes his refraining into a transgression, then indeed they would compel.

But clearly he is forbidden to take a risk (if a Torah-level doubt is treated stringently even in a positive commandment).

All right, I will sum up:
In your view, Rabbi Akiva Eiger is right that someone obligated because of doubt does not discharge one definitely obligated. And that is not because the definitely obligated person judges for himself that the doubtful one is exempt, but because the obligation resting on the doubtful one is not an obligation of Grace after Meals but some "other" obligation under the laws of doubt.
But the religious court may still compel, because in the end some obligation of some kind rests on him.

I understand that there is no such thing as an obligation that is not Grace after Meals (doubts, half-measures, and one witness in matters of prohibition are all the original obligations themselves, and they are drawn after the original obligation). The reason someone obligated because of doubt does not discharge the definitely obligated is that the definitely obligated person judges stringently that the doubtful one is *exempt*. Therefore there is a strong possibility that the religious court also judges stringently that the man is exempt, and therefore it is forbidden to compel. All this is with discharging another's obligation, but the person himself recites the blessing when fulfilling a doubtful commandment because the ruling on the blessing follows the ruling on the commandment.

Just one correction: I did not express a position; I only raised possibilities. I do not have a clear position.

From Rabbi Akiva Eiger's wording it is clear that he understood the matter the way I do.

The language of Pri Chadash, 184: "He must recite the blessing because of doubt, yet he cannot discharge others who definitely did not recite it, because what we hold, that a Torah-level doubt is treated stringently, is only rabbinic as I wrote, etc., and what is only rabbinic cannot discharge a Torah obligation."
This implies that if a Torah-level doubt were treated stringently on the Torah level, then the doubtful obligor would discharge the other.

The language of Rabbi Akiva Eiger, responsa, siman 6: "See Pri Chadash, etc., and simply it would seem that even according to those authorities who hold that a Torah-level doubt is treated stringently by Torah law, nevertheless he is obligated only by reason of doubt, and if so this other person does not fulfill his obligation by hearing him, for he still remains under a doubtful obligation, for perhaps the one discharging him already recited it and he has not fulfilled his obligation by hearing it from him."

Rabbi Akiva Eiger's wording is clear: "for perhaps the one discharging him already recited it." According to your understanding of his position, that reason is not relevant.
And therefore, according to Rabbi Akiva Eiger's own understanding of his position, it would seem more reasonable to say that for precisely the same reason the religious court also does not compel, because perhaps the man already fulfilled his obligation. [Though one could still discuss subtly that perhaps coercion branches out from the commandment like a blessing.] Right?

Not right. On the possibility that the one discharging did not recite it, then even if now he is reciting it only because of the laws of doubt, from the standpoint of the truth it is a full-fledged blessing, and certainly he can discharge the other. So the entire concern is only that perhaps he already recited it. On the possibility that in reality he did already recite it, what he is now reciting is only because of the laws of doubt, and therefore he cannot discharge the one definitely obligated.
But, as stated, I accept all the possibilities, and that is precisely why I do not accept the necessities you wrote.

In this you are right.

By the way, since we are already here, let me make a comment in defense of the honor of Rabbi Shimon Shkop.
In the responsum Yechaveh Da'at he mentioned Sha'arei Yosher and remarked about it that he did not remember the responsum of Ran, siman 51, which says what he says. But Rabbi Shimon there most certainly does mention the responsum of Ran (and in fact he correctly infers from it that its words pose a difficulty against Rabbi Shimon Shkop after deeper analysis, and not as Rabbi Ovadia thought at first glance, that they support him), and he notes that earlier in chapter 2 there he discussed it thoroughly, thoroughly. Rabbi Ovadia apparently did not read all of chapter 8 in Sha'arei Yosher. How could such a significant responsum have escaped the notice of Rabbi Shimon Shkop, whose net was spread from the gates of Jerusalem to the gates of Damascus? Astonishing.

The Ran says there that in a case of doubt whether the vow took effect, he may seek release from it because it is as though it has already taken effect (according to the view that a Torah-level doubt is treated stringently on the Torah level). Rabbi Ovadia understands from this that one obligated because of doubt is now obligated as a certainty. But Rabbi Shimon holds that the obligation as a certainty is a different obligation (an obligation of doubt), not the original obligation. So that if he ate in a case of doubt and it turned out to have been prohibited, he violated two prohibitions: the prohibition itself and the prohibition of doubt (and from this he derives several conclusions there in the chapter). Therefore Rabbi Shimon rightly asks against himself: what does this have to do with the effectuation of the vow?