When ancient texts disagree, what principles can one use to determine which is to be preferred.
Here is one example, but there are many others.
Who are the 'divine sons' being commanded to worship in the LXX Deuteronomy 32:43 textual variant?
What are the sources for the textual variants of Romans 8:1?
I hope that those who have expertise in this field can speak to the issue more generally, offering a summary of principles or references to the same. (I presume the question is not off topic.)
In modern textual criticism there are two broad approaches:
Under this approach, the best/most valuable MSS are those that are the earliest. That is, a text form is deemed more likely to be correct when it is seen in earlier MSS.
Under this assumption, we get the NA28/UBS5 text along with W&H, NIVGNT, SBL, Souter, etc. Most modern Bibles are based on this text.
This assumption simply boils down to choosing the text that occurs most often regardless of when it is found in the textual tradition.
Under this assumption we get the Byzantine text (eg, R&P), Majority text, Orthodox text, F35, etc. I am unaware of any modern Bibles (there may be some) who base their translation on the Byzantine text; however, the Majority Standard Bible and the WEB use the majority text.
The translations based on the TR include KJV (obviously!), NKJV, YLT and several others.
For completeness I should also include a third -
This is also known as "KJV-only-ism". The basis for this text is simply what Erasmus produced in his third edition. In textual form it is, in most places, most similar to the Byzantine text; HOWEVER, it is also a mixture of both the above forms in places, especially in the Gospels.
In truth, it most closely follows the Clementine Vulgate text and often includes portions of Greek text that is not found in any Greek manuscript. Thus, it might be more correctly called the "Clementine Greek Text" form.
[There is a fourth praxis - that of Wilbur N Pickering which he published as "The Greek New Testament According to Family 35" but it is small minority view that need not detain us in a broad-sweep answer like this.]
In deciding which of these bases to follow/adopt, someone wrote (I cannot recall who) that:
Manuscripts must be weighted not counted
This is obviously directed against the majority text methodology. Suffice to say that this subject has a HUGE literature of debate. For a scholarly defense of each position see the following materials:
The most succinct answer to your question is historical context. Without knowing specific determinative information, it's all technically guess work. It's very educated guess work, but still guess work nonetheless. Contextual facts are the only thing that can give you a definitive answer.
I'll give you one example to demonstrate the point.
When dealing with the kings of Judah and Israel during the kings period, there is one king, Omri, who has a variant reading between 1 Kings 16:23 and Josephus, Antiquities 8.312. The former has his reign beginning in the thirty-first year of Asa, the latter in the thirtieth year of Asa.
When you trace Omri's descendants, Ahab, Ahaziah, and Jehoram, you'll find that the house of Omri reigned thirty-nine years with Omri's reign beginning in the thirty-first year of Asa, per 1 Kings, or forty years beginning in the thirtieth year of Asa, per Josephus. When you compare this data to the Mesha Stele, lines 7–8, which states that Omri took possession of the land, and that he and his sons held it for forty years, the historical evidence would suggest that Josephus in this case has the better reading.
Without some basis of fact, it's impossible to definitively say which variant is accurate. But that basis of fact can be the tiniest nuance that no one else notices.
In terms of textual criticism, there are a large number of tried and true rules to weed out the bad readings. It deals with textual families, logical conceptions of human error, and a wide variety of other considerations. For example, textual criticism often considers the more difficult reading to be the more genuine. Logically speaking, copyists who reproduce the text after the fact are more likely to try and clean up or clarify the text than to garble it. It's also more likely for a word to be dropped than added. A dropped word is an unintentional error. A copyist can easily miss a word in the copying process. So when you see a variant like, "Jehoiachin was eighteen years old when he began to reign" (2 Kgs. 24:8), versus, "Jehoiachin was eight years old when he began to reign" (2 Chr. 36:9), the likelihood is that the ten was dropped from the one rather than added to the other. Additionally in a pair of passages such as that, one can also consider the historical context that Jehoiachin made a very adult decision to surrender to Nebuchadnezzar to spare the city and his people (Joseph. AJ 10.100). That's not the act of an eight-year-old.
Ultimately, there are a lot of rules and nuances that go into textual criticism and determining a factual reading. My advice would be to read a few books on textual criticism. And if you're trying to determine between two or more variant readings for a specific passage, research the history and other information relative to the passage in question. Find out if there are any clues that can help you make an educated decision.
The books on textual criticism tend to be from the point of view of someone who has been doing it for 30 to 40 years. Where you can get a rare idea of someone starting out is podcasts with Wesly Huf, who is a Ph.D. student. A good textual critic learns the history of the transmission of the texts. Wes reads the texts from images of the papyrus (the original papyrus when given the opportunity). Thus, he sees what their handwriting was like. He travels to the sites where the texts were found. In a sense many of the podcasts he participated in were like oral exams.
The textual critic does look for the oldest texts, but the oldest text p52 has such a small amount of text that it isn't very useful for textual criticism. What it was useful for was showing an early 2nd century date that preceded the date some had given for when the Gospel of John was written. When I read p52 what struck me was how close the text on the front and back side were to each other. It only made sense for p52 to be from a small codex. This was the first question I asked about on one of Wesley's podcasts. Immediately was rated as a top fan. On another podcast, Wes had said exactly what I asked and even showed an example of the size of the codex. It turns out that Wesley's dissertation is on making measurements of papyrus fragments to determine the form of book the fragment came in. I had given support to his dissertation.
The textual critic will group texts together and look for characteristics of those groups for either making copying mistakes or intentionally altering the text. For example, Alexandrian texts, often the oldest texts because they were commonly found in Egypt, are known to have Alexandrian corrections. What are these? The New Testament was written in Koine Greek, the international language of the first century. For the human authors of the Greek New Testament, Greek was a second language, and it was a second language for most of the readers of the New Testament. Those related to the library in Alexandria were big on classical Greek, so they would make grammatical corrections. Of course, ideally this wouldn't change the meaning. It's like changing ain't to are not in English.
Byzantine texts are notorious for the fear of leaving out something. So, when they saw a variation between two different words they included both words with a καὶ in-between. Hopefully this is enough detail to get the idea, but the main task of the textual critic is attempting to determine what was most likely the cause of a variation and what was least likely to be a correction. That is the task to determine what is most likely the original text.
