I would accept the theory that had the most explanatory power. Or maybe I wouldn't. If a question is so vague and far reaching that there are rival theories each with justification, I'd just conclude the question is irresolvable at this point. But when is anything like that in reality?
If a theory is vague, then a useful criticism is that it's vague, hence it's refuted.
If something is true, all the sciences will converge upon it. If one theory has overwhelming evidence in favour of it and has better explanatory power, obviously I would accept it.
That would be a mistake. You should have a refutation of one of the rival theories. I gave an example of this in an earlier post in this thread regarding the theory that *All swans are white*. If you found 10 white swans, and 1 black swan, does the 10 white swans of evidence "overwhelm" the 1 black swan of evidence? No. So the *amount* of evidence doesn't matter. The evidence either refutes the theory, or it doesn't. It cannot make a positive claim.
And if both theories are criticised?
I'm not sure what you mean. Do you mean unrefuted criticisms?
If you have 2 rival theories, and both theories have unrefuted criticisms of them, then both theories are refuted.
In your own novelty model, where you've defined evidence as such, sure. But that definition of evidence is not currency outside of your personal model. It's just an ad hoc component of your model. There is such a thing as supporting evidence outside of your model, in the real world.
It's not my model. It's the scientific method. It goes like this:
(1) (a) Create a testable theory. (b) Design an experiment that could refute it.
(2) (a) Run the experiment and collect the result -- which is physical evidence. (b) Interpret the result.
If (2b) rules out the theory, then go back to (1a) and create another testable theory — maybe from the refuted testable theory by changing a part of it so that the new version doesn’t contradict the existing evidence.
Note that every step is fallible. So you want to critically question every step. So for (2a), that means that the experiment is repeated many times and by many people.
Topic: Why atheists fail to persuade theists