The Mishna (Kerisus 6:3) records a machlokes between R' Eliezer and the Chachamim whether a person can voluntarily bring an asham taluy. Baba ben Buti, the Mishna tells us, in accordance with R' Eliezer's view would bring an asah talauy every day except the day after Yom Kippur .
The Tiferes Yisrael asks an interesting question. How could Baba ben Buti ignore the majority opinion of the Chachamin in favor of R' Eliezer when the Torah tells us acharei rabim l'hatos? How could the kohanim have accepted his korban on a daily basis when according to the majority view it was chulin b'azarah? Even in the famous debate (Baba Metziya 59) over tanur shel achna'i where R' Eliezer had miracles and a bas kol on his side, the Chachamim rejected his view because majority wins. Not only that, but what is a zakein mamrei if not someone who acts based on his own interpretation of the law in contradiction to the psak of the majority of Sanhedrin?
Why then was R' Eliezer (or Akavya ben Mehalalel in Ediyos 5:7) not a zakein mamrei? The Tif. Yisrael answers that though he disagreed with the majority of the Chachamim in theory, in practice R' Eliezer bowed to their view. Baba ben Buti, however, disagreed in practice. My son did not like this distinction. He pointed out that the gemara (B.M. 59b) says openly that the Chachamim burned the taharos of R' Eliezer, implying that he had relied on his own opinion in practice.
The truth is that we find in other places that individual Tana'im acted in practice based on their own minority view. The gemara tells us that in R' Eliezer's town they would chop wood on Shabbos if needed for milah because he held machshirei milah are doche Shabbos against the majority view; R' Yosi would eat chicken and milk together because he held that there was no rabbinic prohibition of doing so, against the majority view. R' Elchanan in Kuntres Divrei Sofrim explains these cases as having occurred before the issue was formally brought to a vote and decided by the Sanhedrin. In other words, historically there may have been a period of flux during which different traditions were accepted and practiced, some more widely adopted than others, and Sanhedrin took no pains to intervene. Once the issue did come to a vote and was resolved, the minority view became unacceptable in practice. Based on this approach perhaps Baba ben Buti was free to do as he pleased because there had not yet been a formal vote on the issue.
Chazal famously darshen (cited by Rashi in P' Shoftim) that one must obey the Sanhedrin even if they appear mistaken and declare that right is left and left is right. Yet the gemara in Horiyos implies that even a talmid who knows Beis Din is mistaken should not follow their psak. The Ramban in Sefer haMitzvos resolves the contradiction using the same logic as R' Elchanan: Before Beis Din hears out the talmid, he is entitled to stick to his guns and follow his own interpretation irrespective of the majority's disagreement. However, if Beis Din hears out the talmid's objections and formally rejects them and rules otherwise, then the talmid must conform in practice to the psak of the majority or risk being labeled a zakein mamrei.
What remains unclear to me is why certain issues were to be taken to a vote and resolved and other issues remained unresolved. For example, it seems (Chagigah 16) that the issue of whether a korban should get smicha on Yom Tov was debated for centuries. The Margoliyas HaYam in Sanhedrin discusses why this was the case; i.e. why a vote and final psak was not given. Whatever the answer in that particular case (I don't recall his solution offhand), I think the question needs to be raised more broadly and I don't know that we have enough information to formulate an intelligent answer (at least I don't, but mareh mekomos welcome).