The Four Great References (AN 4.180) This question refers to The Four Great References in  Mahāpadesa Sutta (AN 4.180).
In each case, it ends with:

If they’re not included in the discourses and not found in the texts on
monastic training, you should draw the conclusion: ‘Clearly this is
not the word of the Blessed One, the perfected one, the fully awakened
Buddha. It has been incorrectly memorized by ...
If they are included in the discourses and found in the texts on
monastic training, you should draw the conclusion: ‘Clearly this is
the word of the Blessed One, the perfected one, the fully awakened
Buddha. It has been correctly memorized by ...

So, why are there four great references and not one, if the criteria is the same for each of them?
What is the difference between the four great references?
Do they represent primacy or order of reliability? For e.g. is the first great reference more reliable than the second great reference?, is the second more reliable than the third? etc.
If the answer to the previous question is Yes, then does this imply that the traditional commentaries to the suttas by the Sangha is more reliable than the interpretation of a single monk, as suggested by this comment?
This translation (of DN 16) includes this footnote:

In the earlier edition of this work, mahapadesa was rendered as &quot;great authorities.&quot; It is now known that the proper meaning of apadesa is not &quot;authority,&quot; but &quot;reference&quot; or &quot;source.&quot; Besides, from the passage it is clear that there are only two real &quot;authorities&quot; — the Discourses (Suttas) and the Discipline (Vinaya).

The &quot;four&quot; are of course,

Then the Blessed One said: &quot;In this fashion, bhikkhus, a bhikkhu might speak:

'Face to face with the Blessed One, brethren, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation';
or: 'In an abode of such and such a name lives a community with elders and a chief. Face to face with that community, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation';
or: 'In an abode of such and such a name live several bhikkhus who are elders, who are learned, who have accomplished their course, who are preservers of the Dhamma, the Discipline, and the Summaries. Face to face with those elders, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation';
or: 'In an abode of such and such a name lives a single bhikkhu who is an elder, who is learned, who has accomplished his course, who is a preserver of the Dhamma, the Discipline, and the Summaries. Face to face with that elder, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation.'


So, why are there four great references and not one, if the criteria is the same for each of them?
Because they're four different sources from which someone might say they heard something?
Do they represent primacy or order of reliability?
No I read it as explicitly the opposite.
I think the message is that the witness or narrator (IOW any bikkhu after the Buddha's passing) shouldn't be believed unreservedly -- the message might have &quot;been misunderstood by that bhikkhu — or by that community, or by those elders, or by that elder&quot; -- so no matter what source they claim you should measure what they say against the Dhamma and the Discipline, the suttas and the vinaya.
then does this imply that the traditional commentaries to the suttas by the Sangha is more reliable than the interpretation of a single monk
Ha, well I think it's your responsibility to decide for yourself.
On the other hand you're not supposed to split the Sangha, and I think that if a lot of experts seem to disagree with my view then it's likely that I'm missing something -- it's not as if other people's commentaries and so on aren't worthwhile.
I'm sympathetic to the idea that you might not want to trust any one person (even a monk) unreservedly, perhaps especially if what they're teaching is unorthodox.
Even so I think that reasonable people might have different approaches -- this Religious Conservatism discussion starts with,

We need to be clear about what we mean by “a conservative/traditionalist perspective”. For some monasteries it means following the tradition as it has been handed down by their teachers. For others it is about trying to get as close to the intentions of the Buddha as possible. The Ajahn Chah monasteries in the UK - where, incidentally, I have lived - are closer to the former, whereas monasteries such as Bodhinyana are closer to the latter.