1. The day atones partially, and the sent goat achieves full atonement (Tosfos 13a d'ovad)
2. The day atones, but the repentance requirement is waived only if the goat is sent (Ritva)
3. The sent goat atones, but its atonement is due to the power of Yom Kippur day (Tosfos, Rashba)
4. The day atones, but when there is a Bais Hamikdash, it depends on the sent goat being brought (Minchas Chinuch 364)
The Gemora had objected that if one did not repent, the goat cannot atone, as it is a sacrifice of the wicked, which is an abomination. The Ritva explains that Rebbi says that the goat is an exception, and the rule of a sacrifice of the wicked applies only to other sacrifices. The Rashba suggests that since the goat only completes the atonement of the day (following the first explanation above), it is not simply a sacrifice of the wicked, and therefore is effective.
The Gemora introduces a sifra which states that the day of Yom Kippur atones even if the sinner did not commemorate it. The Gemora says that this sifra implies that Yom Kippur atones even without repentance. The Ramban explains that if Yom Kippur needs repentance, it is like any other sacrifice, e.g., chatas, which is not effective if the sinner denies its effectiveness.
Rava says that Rebbi agrees that Yom Kippur does not atone for infractions of the day without repentance. Rava says this must be so, since otherwise there would be no case of one being punished for Yom Kippur prohibitions, since the day itself would atone for them. The Gemora objects, and provides two cases where the day would not atone for the transgression, even if repentance is not generally necessary:
1. The person died choking on food he ate, leaving no time after the transgression for atonement
2. The person ate at the end of the day, leaving no part of the day to atone
Tosfos (13a d'ovad) notes that the goat atones even for sins committed later on the day of Yom Kippur, since otherwise the Gemora should have suggested that the case is one who ate after the goat was sent. Some texts of the Gemora continue by citing a braisa, comparing the atonement of the goat and the day. The braisa states that the goat has the advantage of atoning right away, while the day atones only at the end. The day has the advantage of atoning without a sacrifice, while the goat atones only with a sacrifice. Rashi cites this text and rejects it, noting that it is incompatible with the answers provided by the Gemora, which both imply that any part of the day would atone, not just the end. The Ramban and Rabbeinu Chananel keep the text, and the Ramban explains that this is an alternate answer offered by the Gemora. According to this approach, only the end of the day atones, and therefore one would be liable for violating Yom Kippur if he died before the end of the day.
The Rashba offers two explanations of the advantage of Yom Kippur cited in the braisa:
1. The “sacrifice” refers to sending the goat off the azazel cliff. The braisa refers to this as a “sacrifice” since it is considered a sacrifice like standard ones, and follows its rules.
2. The “sacrifice” refers to the chatas goat whose blood was sprinkled inside the mishkan. The braisa is stating that the atonement of Yom Kippur is independent of this sacrifice, while the sent goat only atones if this sacrifice is also brought.
These two explanations seem to differ as to whether the sent goat is considered a standard sacrifice or not. The answer cited by the Ritva for how the goat atones without repentance seems to consider it a standard sacrifice, while the fact that the goat atones for sins committed later seems to indicate it is not.
The Rambam (Teshuva 1:2) rules that the sent goat atones on all lenient prohibitions (i.e., generic positive and negative commandments) even without repentance, but on all others only with repentance. The commentators attempt to explain the Rambam's source for this ruling, since the Gemora presents the opinions of the Sages, who require repentance, and Rebbi, who does not, with no indication of a middle position. The Lechem Mishne says that the Rambam rules like the Sages, but attempts to limit the extent of the dispute between Rebbi and the Sages. The braisa in which they differ on the explanation of the verse mandating karais is discussing only severe prohibitions, and only in that case do we find the Sages explicitly requiring repentance. The Rambam therefore says that the Sages agree with Rebbi that the sent goat atones for lenient transgressions without repentance. The Meshech Chochma (Vayikra 16:30) explains the Rambam based on the Gemora in Yoma (85b), which says that Rebbi holds that Yom Kippur atones for severe transgressions without repentance, but repentance does not atone for them without Yom Kippur. From here we see that Yom Kippur is more potent that repentance alone. Therefore, the Sages, who say that repentance alone atones for lenient prohibitions, surely say that Yom Kippur alone atones for these.
The Gemora states that an anonymous sifra is Rabbi Yehuda, and therefore proves that Rabbi Yehuda requires repentance for the atonement of Yom Kippur. The Gemora then cites another sifra, which indicates that repentance is not required. Abaye answers that the first sifra is Rabbi Yehuda, while the second is Rebbi. The Ritva asks how Abaye can offer this answer if the Gemora stated that an anonymous sifra is Rabbi Yehuda. He offers two answers:
1. The two sifras are different opinions of Rabbi Yehuda's position. Thus, both follow Rabbi Yehuda, but differ on what Rabbi Yehuda holds on this point.
2. The rule of authorship is a general rule for most sifras, but has exceptions. Similarly, the Gemora identifies anonymous mishnas as Rabbi Meir, since most are, but there are many exceptions to this rule.