Gemara

(Rav Nachman citing Shmuel): When orphans come to divide their father's estate, Beis Din appoints an Apotropos (overseer), and they pick for them a nice share. When they grow up, they can protest (demand a new division);

(Rav Nachman himself): They cannot protest. If they could protest, (the enactment of) Beis Din would be weak!

Kidushin 42a - Question: Elsewhere Rav Nachman is not concerned for the power of Beis Din!

(Mishnah): If Beis Din assessed property (to sell to feed the orphans or widow) for a sixth more or less than the actual value, the sale is void;

R. Shimon ben Gamliel says, the sale stands. If it were void, Beis Din would be weak!

(Rav Nachman): The Halachah follows Chachamim.

Answer: Rav Nachman is concerned for the power of Beis Din only when they did not err.

Question: If they did not err, why can the orphans protest (according to Shmuel)?

Answer: They erred (not about the value, only) about location (e.g. an orphan received a portion far from property that he inherited from his mother's father).

(Rav Gidal): "One Nasi (for each tribe will acquire a portion of Eretz Yisrael for his tribe)" teaches that a Shali'ach can act on behalf of others.

Objection: The Nesi'im could not have been Sheluchim. They acquired also on behalf of minors, who cannot make Sheluchim!

Correction (Rava bar Rav Huna citing Rav Gidal): "One Nasi" teaches that one can acquire to benefit Shimon in Shimon's absence.

Objection: The acquisition of shares of Eretz Yisrael was not beneficial for all. Some people prefer land in the valley, and others prefer in the mountain!

Correction (Rava bar Rav Huna citing Rav Gidal): "One Nasi" teaches that if orphans come to divide their inheritance, Beis Din appoints an Apotropos for them for their benefit and detriment.

Objection: Why should we appoint someone for his detriment?!

Answer: He means, the Apotropos is empowered to do things which may have a detrimental result, if the intent is to benefit the orphans.

Rishonim

The Rif (Kidushin 17a) brings Rav Nachman's enactment and rules like Rav Nachman himself. However, if Beis Din erred about the value the orphans can protest. This is like the Mishnah, which says that if the estimation of Beis Din was a sixth too much or too little the sale is void.

Ran (DH Rav): The Gemara asked why the orphans can protest if Beis Din did not err. This connotes that they can protest if Beis Din erred about the value even less than a sixth. This is unlike the estimation of Beis Din, in which only an error of a sixth nullifies the sale. This is because the Apotropos is like a Shali'ach of Beis Din. However, the Rif says that the orphans can protest an error like the Mishnah, which discusses an error of a sixth! This implies that they cannot protest a smaller error. Also the Rambam says so. Ona'ah (overcharging) does not apply to land when the parties themselves erred, but if a Shali'ach erred this negates his Shelichus. If Beis Din erred less than a sixth, we do not negate what they did, lest this weaken Beis Din.

Tosfos (Gitin 34a DH Beis): We did not say that they erred by less than a sixth, for surely in this case Shmuel would agree that we strengthen the power of Beis Din and do not allow the orphans to protest.

Rambam (Hilchos Nachalos 10:4): If a man left adult and minor orphans and they want to divide their father's estate in order that the adults will receive their shares, Beis Din appoints an Apotropos for the minors and he picks for them the nice share. When they grow up, they cannot protest, for the division was according to Beis Din. If Beis Din underestimated the value by a sixth, they can protest and make a new division after they mature.

Magid Mishneh: 'The division was according to Beis Din' shows that the Rambam holds like R. Tam, who says that the Apotropos divides only according to Beis Din's estimation. This also explains why they cannot protest an error less than a sixth. The Rambam (Hilchos Mechirah 13:9) says that (normally) if an Apotropos erred any amount, the sale is void.

Rambam (Hilchos Malveh u'Loveh 22:15): If Beis Din erred by any amount about the value of land sold to pay a debt, the sale is void.

Question: Why does a division for orphans stand, unless they erred by a sixth?

Answer #1 (Ra'avad): Perhaps here the Rambam discusses when they did not auction the property.

Answer #2 (Kesef Mishneh): The Magid Mishneh suggested that orphans are in place of their father (Beis Din is not their Shali'ach), but Beis Din is like a Shali'ach to sell the borrower's property to pay creditors. He did not like this answer, but it is a proper answer and it fits the Rambam's words.

Answer #3 (Mishneh l'Melech): A division is Beis Din's action; the orphans had no obligation to do so. Paying a debt was the borrower's obligation.

Rosh (Kesuvos 11:18): The Halachah follows Rav Nachman.

Poskim

Shulchan Aruch (CM 289:1): If a man left adult and minor orphans and they want to divide their father's estate in order that the adults will receive their shares, Beis Din appoints an Apotropos for the minors and he picks for them the nice share. When they grow up, they cannot protest, for the division was according to Beis Din. If Beis Din underestimated the value by a sixth, they can protest and make a new division after they mature.

Beis Yosef (DH ha'Achin): It is known that the Halachah follows Rav Nachman in monetary laws.

Shach (2): The Ritva (Kidushin 42a DH v'Im) rules like Shmuel.

SMA (3): Normally, if there is an error of a sixth the difference is returned but the sale stands. We are more stringent about orphans.

SMA (4): If Beis Din realizes the error before they mature, they divide again immediately. The Shulchan Aruch discusses the usual case. Most people do not check to see if Beis Din erred, but the orphans themselves do.