Gemara

(Beraisa - R. Eliezer): A Yavam can annul the vows of a Yevamah, whether there are one or two Yevamim...

(R. Ami): The case is, he gave a Ma'amar. This is like Beis Shamai, who say that a Ma'amar acquires totally.

If Ma'amar makes Nisu'in, this explains why he can annul her vows. But if it makes only Kidushin why can he?!

(Mishnah): The father and husband of a Na'arah Me'orasah (together) can annul her vows.

Rejection (Rav Nachman bar Yitzchak): (Perhaps Ma'amar makes Kidushin.) R. Eliezer said that he can annul her vows, i.e. together with her father!

Question: But the Beraisa says 'he annuls', not 'they annul'!

Answer: You must say that she took him to Beis Din (because he did not want to do Yibum nor Chalitzah), and Beis Din obligated him to feed her;

(Rav Pinchas): A woman vows on condition that her husband will approve. (Here, since the Yavam feeds her, she vows on condition that he will approve.)

Rishonim

Ramban (Gitin 35b DH v'Yesh Omrim d'Chi): A Neder b'Rabim cannot be permitted, not even by her husband. Some say that nevertheless a husband can annul a Neder Al Da'as Rabim, even though it is more stringent! This is because a woman vows on condition that her husband will approve. Even though the Rabim say that they make her vow on their Da'as, really she vow on her husband's Da'as. A Neder b'Rabim is more powerful, therefore a Chacham cannot permit it, and the same applies to her husband.

Rosh (Gitin 4:8): A husband can annul his wife's vow even if it was Al Da'as Rabim. This is because a woman vows on condition that her husband will approve, and she cannot uproot his Da'as and make her vow contingent on others' Da'as. Likewise, she cannot say that she does not want him to annul her vow. Perhaps this is even if he authorizes her, because a Stam woman vows on condition that her husband will approve and the Torah authorized him to annul. Therefore, he can retract his authorization.

Shach (YD 228:76): The Bach says that the Rosh was unsure about this (he said 'perhaps'), but the Tur and all the Poskim bring it l'Halachah.

Ritva (Gitin 83b DH Kol): Even if she says that she does not want him to annul, we know that really she does not want a vow against his will. Also, the Torah authorized him to annul in every case.

Rosh (Teshuvah 10:3, cited in Gra YD 228:103): One cannot stipulate to permit his own vow when he wants. Even if he stipulated that someone else will be able to permit it, this does not help. Once it is Chal, a Chacham or three commoners are needed to permit it.

Rashba (Yevamos 90b DH Kedei): Normally, a woman vows on condition that her husband will approve, i.e. she does not want her vow to stand if it will make her repulsive to him. When he must divorce her, this does not apply.

Me'iri (Shabbos 46b DH b'Maseches): If a husband annulled his wife's vow on Shabbos, the food is not Muktzeh. A woman vows on condition that her husband will approve, i.e. she expects him to annul it, and expected to eat the food.

Ritva (Kesuvos 59a DH R. Yochanan): How can a husband annul a vow that was not Chal yet? Now, it is not Inuy Nefesh or Devarim she'Beino l'Veinah! Tosfos says that even in such a case, a woman vows on condition that her husband will approve.

Ran (Nedarim 73b DH v'Ha and DH v'Ika): Even though the Gemara says that R. Eliezer holds like Rav Pinchas, all agree to Rav Pinchas. The Gemara in Nidah says that a husband can annul vows of a girl married to him mid'Rabanan, due to Pinchas' law. However, in any case he must annul using the words that the Torah specified (Hafarah, not Hatarah).

Tosfos (Yevamos 89a DH Mai): Some texts (on 90b) say 'why did Chachamim say (in some cases in which a husband cannot annul mid'Oraisa) that a husband can annul (mid'Rabanan)?' They were able to do so because a woman vows on condition that her husband will approve.

Rivash (370): R. Shimshon says that if a Chacham knows that Levi regrets his vow, he can permit it without Levi's Da'as. We learn from Hafaras ha'Ba'al, which is just like Hataras Chacham, except for the words used to permit. The Gemara (Kidushin 81b) explicitly says that a husband can annul without his wife's Da'as.

Rebuttal (Mishneh l'Melech Shavu'os 6:4): Hafaras ha'Ba'al is different, because a woman vows on condition that her husband will approve.

Poskim

Shulchan Aruch (YD 228:24): A husband can annul what his wife vowed Al Da'as Rabim, even for Reshus (not a Mitzvah).

Beis Yosef (DH u'Mah she'Chosav v'Yesh): We permit Cheremos of the Tzibur even though they were made Al Da'as Rabim. It is as if they stipulated to forbid until they want to permit it, just like a woman vows on condition that her husband will approve. Therefore, they are permitted for the future but not retroactively, the Tzibur need not be there when it is permitted, we can permit them even if the reason for the Cherem still applies, even within the time the Cherem was supposed to last or before it took effect.

Shulchan Aruch (37): If Reuven vowed not to do something Al Da'as Shimon, even if Shimon permits it Reuven needs three commoners to permit his vow, unless he says that he intended that Shimon will be able to permit it.

Ramban (Mishpat ha'Cherem DH v'Omer)): If Reuven vowed Al Da'as Shimon, he meant that Shimon will confirm it or be silent when he hears it. We learn from Rav Pinchas. If Shimon did not protest immediately, the vow is confirmed. Even though a husband has the entire day to annul it, this is a Gezeras ha'Kasuv for Shalom Bayis. It does not apply to others. A proof is that the husband cannot annul even the same day after divorcing her. Even though she vowed Al Da'ato, the Chidush that he can annul applies only when she is in his Reshus.

Rebuttal #1 (Rivash 407, cited in Beis Yosef DH Kosav veha'Rivash): Shimon must Mevatel verbally, just like a husband. However, the comparison is not simple. Perhaps 'Al Da'as Shimon' only means that Shimon will explain it, to prevent Reuven from giving improper interpretations of what he meant. This is like we tell one who must swear, 'you do not swear Al Da'atcha, rather, Al Da'ateinu and Al Da'as Beis Din' (Shevu'os 29a). Also, if we could learn from Hafaras ha'Ba'al, it should not matter which word he uses (Heter or Hafarah), as long as he reveals that he disapproves. Also, the husband can annul even if she says that it is not Al Da'ato! Rather, it is a Gezeras ha'Kasuv and we cannot learn from it. However, if Reuven later explains that he made it contingent on Shimon's approval, we heed him. We are stringent about unexplained Nedarim, and lenient to believe the explanation (Nedarim 18b).

Rebuttal #2 (Ran Nedarim 73b DH Ika): Hafaras ha'Ba'al is a Gezeras ha'Kasuv. Rav Pinchas explains why the Torah gave to him this power. It does not apply to one who said 'I vow Al Da'as Shimon', unless he specified 'my vow is valid only if he will approve'.

Beis Yosef (DH v'Rabbeinu): The Tur and Rosh (Teshuvah 10:3) are stringent even when Reuven stipulated that Shimon should be able to annul the vow.

Chasam Sofer (2 YD 321 DH v'Acharei): Since a woman vows on condition that her husband will approve, it suffices for him to reveal that he disapproves. Nevertheless, we learn from "V'Ishah Yeferenu" that he cannot make a Shali'ach to annul.