In his opening comment on the parsha, Rashi points out (quoting the tana'im) that the correct location of the Sanhedrin is in the Beis Hamikdosh. The particular room (known as the lishkas hagazis) in which they met during the period of Bayis Sheini was divided into two parts. One half was sanctified with the kedusha of the azarah, while the other half only had the kedusha of the har habayis. No one may sit in the azarah except for a king who is a descendant of malchus Beis Dovid. Even the seventy one members of the Sanhedrin had to be careful to only sit in the half of the room which did not have kedushas ha'azarah.
According to Talmudic tradition (Yoma 52), the possuk in Divrei Hayomim (II, 35:3) reports that towards the end of Bayis Rishon Yoshiyahu haMelech instructed the Leviim to remove the aron kodesh, with the luchos in it, from the kodesh hakodoshim and place it in the basement in a special vault specially designated for this purpose from the days of Shlomo Hamelech. The reason for this move is given in Divrei Hayomim but is very unclear. The Netziv (in his introduction to his commentary on the Sheiltos) understood this as follows:
Ramban writes (Devarim 17:11) that the need for the Sanhedrin to meet in that special location was in order that they should be close to the aron with the luchos. This proximity was to ensure that the Sanhedrin should have divine assistance in paskening shaylos. In he days of Yoshiyahu haMelech they were not yet afraid that the Beis Hamikdh would be destroyed and the aron would be taken into captivity; that concern only began years later. What motivated the removing of the aron with the luchos was that the rabbonim realized that there would soon come a time when they would no longer have this heavy siyata d'shmaya in the area of psak, and would have to work hard with much pilpula shel Torah to arrive at a proper conclusion, so they decided to start practicing this new style of psak by removing the aron with the luchos.
Even after this major change, our ability to rely on the psak of a human being is still based on the assumption that "sod Hashen leyerai'av" (Tehilim 25:14). Whenever we don't know one way or another, we should assume that a talmid chacham who is God fearing has had divine assistance to pasken properly. When the Sanhedrin sat in their office near the aron with luchos we assumed that they had an even stronger degree of siyata dishmaya not to err. Whether during the earlier years of the first Beis Hamikdash (when the aron was in the kodesh hakodoshim), during the period of the second Beis Hamikdash (when the aron was in the specially designed vault in the basement), or nowadays (when the rabbonim are nowhere near the aron at all) the right (and the obligation) to assume that the psak of a rabbi is not in error is certainly based on the supernatural assumption that the rov was granted divine assistance not to err.
Some mistakenly think that this notion contradicts the principle "lo bashomayimn he - the Torah is no longer in heaven", i.e. once Hakadosh Baruch Hu "gave" the Torah to Moshe at Har Sinai He no longer gets involved in determining any psak Halacha. This is not correct! The Talmud invokes lo bashomayim he to explain why we can not have a navi tell us, by way of explicit prophecy, what the halacha should be; or that we would not be swayed by a bas kol from heaven on a matter of psak halacha. We still recognize, however, that human beings are fallible, and as such the only reason any psak from any rov may be relied upon is because we have the right to assume that the rov, if he is a yorei shomayim, must have had divine assistance to pasken correctly without erring.
The Talmud notes that one reason we follow the opinions of Beis Hillel is because they were more humble than Beis Shamai. The Talmud doesn't state that Beis Shamai were arrogant, rather that Beis Hillel were humble. What does humility have to do with psak halacha? Perhaps the humble person ought to be granted a middos award, but why ought the reward be that his opinion is accepted halacha lmaaseh?
The answer apparently is that the navi Yeshaya (57:15) tells us that Hakadosh Baruch Hu chooses to be with the humble people. Therefore, the anav stands a better chance of having that divine assistance to be mechavein l'amita shel Torah. When following the instruction of the mishna in Avos to choose a rov to follow in matters of halacha we must try to choose an intelligent, learned, honest rov who also posses yiras shomayim and humility. These last two qualities are essential to be more secure in the knowledge that the particular talmid chacham who is issuing the psak will be granted siyata dishmaya not to err.
The famous tanna R' Eliezer ben Horkenus is often referred to as R' Eliezer Hagadol, and the Talmud Yerushalmi comments that the appellation "hagadol" means that R' Eliezer was unusually humble. In v'yiten lecha (recited in many shuls on motsaei Shabbos) we recite the Talmudic statement, based on the passuk in Yeshaya alluded to above, that whenever we read in Tanach about the "gedula - all-powerfulness" of Hashem, the passuk will always mention His humility. The real gadol must be humble.