Gemara

If the Ba'al (who was Makdish) offers 20 to redeem it and someone else offers 26, if the Ba'al wants to redeem it for 31 Sela'im and a Dinar, he has precedence. If not, the other redeems it for 26.

Nedarim 36b - Question: Does one need Shimon's consent to separate Terumah for him?

Since this is Zechus for Shimon, his consent is not needed;

Or, perhaps he prefers to do the Mitzvah himself!

Kesuvos 11a (Rav Huna): If a minor wants to convert, we immerse him (to convert him) on the Da'as (intent) of Beis Din.

Question: A Mishnah already teaches this!

(Mishnah): Zachin l'Adam she'Lo b'Fanav (we may do something beneficial for a person in his absence) but we cannot do Chov (something detrimental) to him in his absence.

Kidushin 29a (Mishnah): A man must redeem his (firstborn) son.

If the father does not, the son must redeem himself. We learn from "Pado Sifdeh".

Rishonim

Question (in Rivash 131): Why does the Rambam say to bless 'Al Pidyon ha'Ben' when redeeming his son? The Mitzvah is on the father. We expound that if one was not redeemed, he has a Mitzvah to redeem himself. There is no Mitzvah through a Shali'ach or through Beis Din...

Tosfos (Kesuvos 11a DH): Some texts in Bava Metzia (71b) say 'a minor (has no Shelichus, but he) has Zechiyah', and do not say 'mid'Rabanan'. We can say that it is mid'Oraisa. If a minor Nochri comes to convert, we consider him like a minor Yisrael, Even though Zechiyah is due to Shelichus, and mid'Oraisa he has no Shelichus, that is only in matters with a little Chov, e.g. to separate Ma'aser. Perhaps he would have wanted to exempt everything with one grain of wheat, or he wanted to give more! Conversion is total Zechus, so he has Shelichus.

Poskim

Rema (YD 305:10): The father cannot redeem through a Shali'ach. Beis Din cannot redeem the son without the father.

Taz (11): Tzedah l'Derech (Parshas Bo) concluded that if the father died before 30 days, the grandfather or Beis Din can redeem. He brought proofs, and testified that the Maharal of Prague ruled like this. He is correct. The Maharshal brings from Me'il Tzedek 'if the father is not in the city, someone else can redeem the Bechor, for one's Shali'ach is like himself.' The Maharshal comments that if the father is in the city, someone else cannot redeem without the father's Da'as (knowledge or consent).

Taz: I say that if the father died, Beis Din cannot redeem and acquire the money for the Kohen. Tzedah l'Derech proved from Nedarim 36 (that Beis Din can). I learn oppositely from there! The Gemara asked whether one needs Shimon's consent to separate Terumah for him. Since it is Zechus for Shimon, his consent is not needed. Or, perhaps he prefers to do the Mitzvah himself! The question was not settled. The Shulchan Aruch and Rambam rule that it is valid Terumah. One need not inform him. Tzedah l'Derech derived that similarly, one may give his own money for Pidyon ha'Ben. It is Zechus for the baby.

Rebuttal (Taz): Tosfos says that a minor has no Shelichus when there is a little Chov. He did not say 'when there is (Stam) Chov.' I.e. since we find Shelichus for a minor only in this matter (conversion), this shows that it is only in such a case, when there is no Chov at all. If there is a little Chov, for an adult we would ignore it, since there is more Zechus. One can be a Shali'ach for a minor only if it is pure Zechus. In Nedarim we say that one can take Terumah for another, i.e. for an adult. It is a small Chov to deprive the owner of the Mitzvah. For a minor, Zachin l'Adam she'Lo Befanav does not apply, since it is not pure Zechus. Even when a minor is here, it is as if he is not here (for he lacks Da'as). The same applies to Pidyon ha'Ben. Another cannot be a Shali'ach for a minor, for there is a little Chov, i.e. he loses the Mitzvah. Tzedah l'Derech also brought proofs from the first Perek of Kidushin (that one may redeem without the father's appointment). Really, they prove oppositely. As long as the father is alive, he could be a Shali'ach to redeem his son in place of him (the son). Therefore, the grandfather is like his father. We do not follow the questioner in the Rivash. The Rivash did not bother to refute him. If the father died, one may redeem the son until he matures. The Maharil says so.

Rebuttal (Nekudas ha'Kesef): Kesuvos 11a proves that Tzedah l'Derech is correct. We immerse a minor to convert him, due to Zachin l'Adam. Do not say that here there is some Chov, for he wants to do the Mitzvah himself. The Rambam, Semag and Tur rule that one can take Terumah on behalf of another due to Zachin l'Adam. This shows that we do not consider it Chov to do another's Mitzvah. Tosfos says that the Chov of Terumah is that perhaps the owner wanted to give more or less. Also, Tosfos says that converting a minor is pure Zechus. We do not say that he would prefer to convert himself when he matures. Also, there is some Chov only regarding Terumah, in which the Shali'ach uses his own produce to exempt the owner's. Here, Beis Din acquires the money to the minor, through Zachin l'Adam, so we redeem him with his own money. The Chov of Terumah is giving this is wrong amount, i.e. when we are Zocheh the produce to the minor before making it Terumah. The Gemara in Nedarim asked about without Zechiyah. Even if that question was not resolved, we can do Pidyon ha'Ben if we are Zocheh the money to him first, In Gitin (42a), we say that an Apotropos (of minors) takes Terumah for them. The Rashba explains it is a mere decree that he can be Torem only what they need to eat now, lest he err. Letter of the law, the Apotropos could tithe. We do not say that the minors want to tithe when they mature! Since he tithes from their Peros, it is their Mitzvah.

Shach (11): Tzedah l'Derech says that even the Rivash said only that the Torah did not obligate others to be a Shali'ach for the father, but if the father does not want to redeem, or he died, even Beis Din need not become Sheluchim in place of him. Surely Beis Din can redeem without the father if the father transgressed and did not redeem, or he died before redeeming. All the more so the grandfather can redeem in such a case. Ma'adanei Melech says that Beis Din cannot redeem if the father died, as long as the son is a minor. We need not say so.

Chasam Sofer (YD 297): Shelichus of sending the father's money to a Kohen is like sending it on a monkey. He informs the Kohen that it is for Pidyon ha'Ben, and he is Yotzei. No one would say that a Shali'ach does not work for this. Poskim argue about a Shali'ach who gives his own money, without acquiring it for the father. This is like separating one's produce to be Terumah for another's. The questioner in the Rivash was sure that this does not work. Many erred greatly about this. If there is no father, Beis Din redeems with the Tzibur's money. This is a separate Mitzvas Aseh.

Pischei Teshuvah (16): Even if Shelichus does not take effect within 30 days, the Shali'ach can redeem (after 30 days) due to Zachin l'Adam, since we know that the father wants this! The Chasam Sofer (2:296) concluded that a Tzibur of Leviyim must redeem Bechorei Yisrael (who were not redeemed). Yeri'os ha'Ohel refuted the Nekudas ha'Kesef's proofs, and concluded like the Taz. The Chasam Sofer (295) concluded that it is best to be concerned for the Taz, and redeem without a Berachah, and put a silver plate on him saying 'Safek redeemed', so he will redeem himself when he matures. Chemdas Shlomo says that it is best to be passive. However, since the Shach says that usually, the plate is lost, and the Mitzvah is not done. To fulfill all opinions, we hang a plate on him saying 'not redeemed', and redeem on condition that when he matures he will not know that he was not redeemed and he will not redeem himself. If not, the money given now is a gift. The Gaon of Lisa says that we cannot stipulate that the minor's money should be a gift (if the minor will forget later), and it does not help with others' money, unless we are Mezakeh them to the minor on condition to redeem with them.

Gra (17): Even another can redeem without the father's Da'as, like we say about Pidyon of Ma'aser Sheni, Neta Revai and Hekdesh. All the more so, another can do so here, for it is like a mere debt. The Kohen can collect from Meshu'abadim (property that was sold). If one pays another's debt, the borrower is exempt, just l'Chatchilah it is a bigger Mitzvah for the father to redeem. This is like Milah and other matters that the father is obligated to do. We need not say that the Rivash agreed to the questioner.

Chazon Ish (YD 185 DH v'Ikar): It seems that the Gra's proof from Hekdesh is from Erchin 27a, which says that if others offer more, they have precedence. However, what is the source that we do not need the owner's Da'as? Perhaps regarding Ma'aser Sheni the owner may not redeem for less (than others offer), and he must sell it to another or give more to redeem it! We can say the same about Hekdesh. However, regarding Hekdesh it is reasonable not to require his Da'as, since he has no stake in (what he made) Hekdesh, just it is a Mitzvah for him to redeem it. Tosfos holds that one may redeem another's Ma'aser only with his Da'as, if not for Zachin l'Adam. The Gra connotes that it is even b'Al Korcho of the owner. This cannot be. Surely, if the father protests, one cannot redeem his son b'Al Korcho! I do not understand the comparison. If one gives money for Pidyon ha'Ben, still the father (or Bechor) redeems. Anyone may redeem Ma'aser Sheni or Hekdesh for himself; but for Ma'aser, he needs the owner's permission. Also, being a debt is not a reason not to require the father's Da'as. Here it is a Mitzvah! One may pay another's debt because it is a Zechus. If he protests, one cannot pay for him. If the lender pardons the debt, that is his choice; he can do so b'Al Korcho of the borrower.