Gemara

(Beraisa): If one wants to burn it (a Pesach that became mostly Tamei) in front of the Mikdash using his own wood, we do not accede.

(Rav Yosef): This is to spare from embarrassment one who does not have wood.

Bava Basra 120a: When the Torah discusses Tzelafchad's daughters marrying, it lists them in order of their age. Here (when they asked for an inheritance), it lists them according to their Chachmah! This supports R. Ami:

(R. Ami): In Yeshivah, we give priority to the greatest Chacham. In Mesibah (a banquet), first priority is to the oldest.

(Rav Ashi): This is only if he is extremely Chacham or old.

Rejection (of support - Tana d'Vei R. Yishmael): "Va'Tihyenah (they were)" - Tzelafchad's daughters were equal in Chachmah.

Rishonim

Rif and Rosh (Kidushin 14a and 1:54): In matters of Yeshivah, we give priority to the greatest Chacham. In Mesibah, first priority is to the oldest. This is only if he is extremely Chacham or old.

Rosh (ibid.): The Rashbam explains that "Yeshivah" refers to judgment or other matters of Torah. The [greater] Chacham has precedence. Mesibah is a banquet, and the same applies to Nisu'in, like Tzelafchad's daughters. If the elder is exceedingly old, he has precedence regarding Mesibah, since he is somewhat Chacham. If not, the outstanding Chacham comes first. We learn from here that if the Chacham is exceedingly Chacham, and the elder is not exceedingly old, the Chacham has precedence even for Mesibah. If the Chacham is not exceedingly Chacham, and the elder is exceedingly old, the elder always has precedence, as long as he is somewhat Chacham. If neither is exceedingly Chacham or old, I say that we always follow age. Rav Ashi said that we distinguish Mesibah from Yeshivah when both are outstanding. This implies that if neither is outstanding, we always follow one of them. Since he did not specify, we follow age. Greater Chachmah of the Chacham is not a reason to shame the elder. The Chacham is not shamed. It is known that we honor the elder due to his age!

Ran (DH v'Hu): Rashi (perhaps this should say Rashbam - PF) says that if neither is outstanding, the elder has precedence. Others say that it is as if both are outstanding, and in Yeshivah the Chacham comes first, and in Mesibah the elder comes first.

Beis Yosef (YD Sof Siman 244): In Bava Basra 120b, Chidushei ha'Ran (DH bi'Yshiva) brought this in the name of the Ro'oh.

Rambam (Hilchos Sanhedrin 1:3): The Av Beis Din sits to the Nasi's right. The others sit in front of him according to their years and level. Whoever is greater in Chachmah is closer to the Nasi from his left.

Kesef Mishneh: First the Rambam says that the others sit according to their years and level. Then he says "whoever is greater in Chachmah is closer to the Nasi"! It seems that "according to their level" refers to their level of Chachmah. He says that "whoever is greater in Chachmah is closer" when they are the same age.

Aruch ha'Shulchan (CM 1:15): Even though in YD 244 (brought below) we say that for Torah, Chachmah overrides age, the entire Sanhedrin is considered outstanding in Chachmah, so no one is much greater than another. Therefore, they sit according to age.

Chikrei Lev (4, Shiyurei OC 136:7, DH Od): This is opposite to R. Ami's teaching! We must say that they are not greatly different in Chachmah. He holds like the Rashbam, that in such a case we follow age, unlike the Ro'oh. I would say unlike the Kesef Mishneh. Rather, we follow years when they are equal in Chachmah. When they are different in Chachmah, we follow Chachmah.

Rambam (7): We seat the three rows of Talmidim in front of a Sanhedrin. In each row they sit according to their level of Chachmah.

Or Some'ach: He learned from Bava Basra 120a.

Teshuvas ha'Rosh (5:3): The Gadol sits at the head, and regarding Mesibah the elder has precedence. These do not refer to a fixed place in the Beis ha'Keneses. One bequeaths it to his sons. If a Gadol sat at the head, and his son was lowly, must he abandon his father's place and seat a Gadol in his place?! No. One inherits his father's place, even if he is not as great as his father.

Mahari Bei Rav (50): Reuven inherited a place in the Beis ha'Keneses from his father and sat there for 60 years. He died, and his [only] son Shimon wants to sit there. David objected, because he is older than Shimon, and it is improper for a younger man to sit in front of him. This is not a claim. There is a Mitzvah to honor elders, but not when there is monetary loss (Kidushin 32b). Even to honor parents, one need not spend his own money.

Rashbam (120a DH Shekulos): The Torah lists the daughters in different orders to teach that they were equal. There is no support for R. Ami.

Ritva (120a DH bi'Yeshiva): If the elder is not somewhat Chacham, even a Chacham Mamzer comes before an Am ha'Aretz Kohen Gadol (Horayos 13a)! If neither is outstanding, the Chacham has precedence even for Mesibah.

Tosfos (Yoma 13a DH Halachah): Why does the Gemara rule like R. Yosi about one who substituted for a Kohen Gadol? This will not be relevant until Mashi'ach! Actually, it affects a leader of the Tzibur who stepped down due to Ones. When the Ones passes, he returns to his position, and we honor also the one who substituted for him, like R. Elazar ben Azaryah, who substituted as Nasi in place of R. Gamliel.

Poskim

Shulchan Aruch (YD 244:18): If a young outstanding Chacham is with a moderate Chacham who is very old, regarding sitting in judgment or Torah, we seat the bigger Chacham at the head, and he speaks first. At a drinking fest or wedding feast, we follow seniority and seat the oldest at the head. If the younger is an outstanding Chacham, and the elder is not so old, the Chacham always comes first.

Gra (21): In both cases, we taught that he must be outstanding. This implies that if only one of them is outstanding, he has precedence in every case.

Shulchan Aruch (ibid.): If the elder is exceedingly old, and the Chacham is not so outstanding, the elder always comes first, since he is somewhat Chacham. If neither is so Chacham or so old, the elder is first in every case.

Taz (10): Also here we must say that he is somewhat Chacham, like in the Reisha. This is all the more so! Why did he need to teach about when the elder is exceedingly old, and the Chacham is not exceedingly Chacham? If the elder always has precedence when neither is outstanding, all the more so when only the elder is outstanding! I answer that we must teach that even so, he must be somewhat Chacham (Maharshal). The Rashbam in Bava Basra regarding Tzelafchad's daughters connotes that we follow the elder even if he is not 70, because it does not shame the Chacham.

Gra (22): Do not say that when neither is outstanding, it is like when both are outstanding. If so, why does it say "he must be outstanding"? We should have taught this case (when neither is outstanding)!

Gilyon Maharsha: Tosfos (Yoma 13a and Zevachim 45a DH Hilchesa) says that if a leader or Rosh Yeshiva stepped down due to Ones, when the Ones passes, we honor also the substitute.

Note: Perhaps "also" connotes that we honor the first more, just like when R. Gamliel was reinstated, he led the academy three times as often as R. Elazar ben Azaryah did.

Omer ha'Shichchah (Bava Basra 126): Why did the Rambam omit this law? Perhaps he holds that since R. Yishmael taught that Tzelafchad's daughters were equal, this suggests that he argues with R. Ami. The Rashbam says that R. Yishmael does not support R. Ami.

Chikrei Lev (ibid., DH Ela d'Achti): How can we learn from Tzelafchad's daughters? They were litigants. It is not relevant to seat them according to Chachmah! Rather, the Torah changes the order in which it lists them to teach that we do not always follow age. Rather, sometimes we follow Chachmah. The Torah authorized Chachamim to decide when to follow each, like the Ran (Yoma 1a) says about Inuy (affliction) of Yom Kipur.