There is really no authority, because everyone can interpret the Tanach for themselves. The other problem is that it doesn't have historic continuity. After the destruction of the second Temple, the Sadducees pretty much died out and then history didn't see "scripture-only" movements within Judaism until around the 10th century when Karaism was started. Plus, correct me if I'm wrong, but I think the Sadducees only followed the 5 books of the Torah, whereas the Karaites follow the full Tanach that was accepted by regular Orthodox Jews.
That is not true, we can't distrot the torah for our needs, while we trying to clarify a verse from the tanakh we need allways remember that what G-d said is the most importent and the human needs should be throwed out the window .
The first Jews that puted Tphilin on tham, and therefor believed in so called "Oral Torah" were a cult name Pharisees that was created in the 2 centery B.C.E., their named Pharisees (Prushim in hebrew) because they leaved the mainstreem of Judaism in those days, that didn't believed in what we know today as Oral Torah, they, the Pharisees (wich are the base for today's orthodox judaism) said they are the only one that they and only they have the right to try and clarify verses from the Tanakh, and their "clarify verses" are what we know today as the Talmud .
I don't know how they had no shame to claim only they have the right to try and clarify verses from the Tanakh, because their number was only 6000 !!!
The other jews didn't believed in the Oral Torah AT ALL.
After the Bar Kochva rebelion the Pharisees became very strong and actually ruled the Jewish way of thought, but the original Jews were never destroyd, and in the 8th centery B.C.E. a non-believer of the Oral Torah name Anan ben David decided to unite all jews that didn't believed in the Oral Torah, later only the Karaite Judaism have been created that their goal is to make the jewish people come back to his original believes .
Actually, the "Jewish principles of faith" that the Rambam mantiond were the SAME Jewish principles of faith that a karaite rav name Yehuda ben Eliyahu Hadassi mantiond while the Rambam was only 13 years old, that means that the karaites were first to know what are the most important thing in Judaism .