Currently I am reading "History as Propaganda: Tibetan Exiles versus the People's Republic of China" by John Powers on assignment from a class, and while reading I was struck by just how far the disagreement over Tibetan history goes between pro-Chinese and pro-Tibetan authors. I understand that bias, or outright lies, exist and may be proven false through better use of evidence, but some of the disputes seem to be about rather mundane events. Others seem to deal with how either side at the time interpreted the nature of the same events and relationships. On either side exaggeration or outright lies and propaganda can be dismissed, but that still seems to leave much disagreement.
However, my question does not so much concern this specific dispute as with how historians deal with any such dispute. If an event has multiple interpretations which can not be proven to be false or likely false, then it would seem that those looking into that event (historian or not) can either select an agreeable narrative, or must live with uncertainty.
Therefore, how do historians deal with any such dispute which has multiple narratives which are within the realm of possibility, yet nonetheless incompatible? What kind of facts are useful for helping find which narrative is true, or most true?
Also, I apologize if this is off topic, as it's not so much a question about history as how to practice history.
Often, one of the ways to begin is to identify what is at stake in the dispute: which other, important questions would be affected by how/whether we settle this one?
For example, let's say we have a common problem, a dispute whether Country A or Country B "started" a particular war in the past. If you want to write a book about the attitude of Country A toward aggressive foreign policy or something like that, it may be very important that you figure out which side of that argument you are on and take a stand, because the answer could make the difference between your arguing that Country A was excited about aggressive war and thought it was good for the glory of the homeland, versus if you decide that Country B was the aggressor, you might argue that Country A didn't really like aggressive war at all and only used that rhetoric later to stir up moral for the war with Country B. Before you can start that book, you need to figure out what you believe the answer is and be able to make a convincing case for why the other people are wrong, or your whole argument won't make any sense.
On the other hand, if you want to write about the economic effect of the war on Country A, you might not really need to decide who started the war, because the point is however it started, it eventually happened and you're interested in the results. You might want to acknowledge that there is a debate about how the war started, and if you think one side is right you might say so, but you shouldn't need to get into it very much because it wouldn't change your argument either way.
So historians don't just "select an agreeable narrative," we read the sources, and decide what seems most likely. We do live with some uncertainty, because usually everyone we study is dead and can't tell us for sure. But if you read documents closely, you will often become persuaded that one interpretation makes the most sense, and then you can write about it and try to persuade everyone else. Or you can decide that a particular argument between historians doesn't actually matter for what you want to do (like the economic impact example) and then you can write about something else and try to move the conversation toward your questions instead.