[...] Then, since storytelling is a form of communication and the intent of all communication is to share information, the most useful interpretation is the one with the best information that the most people can understand.Ideas necessarily exist independent of utility, and as such, can only 'gain' it through application. Application in this case, as near as I can see, is use of the interpretation of others as a medium for understanding of larger things, and as such, validity (utility) is indeed not infinite but is instead limited to a generalized palette. Thus, if Janet is a paranoid schizophrenic who interprets the rabbit hole as a metaphor for her personal hell of persecution by rabbits and clocks, her interpretation is fantastically useless in analyzing the text. Valid, but useless, as stated in the comment above.
I'll leave you to determine what makes some info better than other info, but at least by looking at it from this standpoint we can say that yes, all interpretations are valid but not all are equally useful.
In other words, why talk about what Janet thinks of Alice in Wonderland if what Janet thinks has little utility to us?
However, how might one determine that her interpretation is, in fact, useless, if not exactly invalid? We have no a priori knowledge of this interpretation.
Basically, this is the process of deciding an interpretation. See the image to the left: moving from 1 to 3 results in something that is easy to understand, a 'natural' progression that is anything but natural, but has the advantage of avoiding an overcomplicated explanation of every other possible 'end' result. I believe that we do this every time we interpret something, and therefore end up presenting 3 as a completed interpretation, having pared a massive tree down to something more manageable. (image modified from this)
B could be any one of the end points and 3 would always end up looking the same; that is, all are valid, because the process of creating an interpretation is identical in all cases. But is it useful? We cannot tell until we see where A and B were, originally. Without a priori knowledge of the interpretation, we only have 3 to go by.
My god, the point, finally: if interpretations are presented to the world as #3, knowledge of other interpretations can help shape a more complete knowledge of #1. As long as Janet arrives at B from A along a path that can be abstracted to #3, the interpretation is both useful AND valid. In fact, assuming adherence to the text and analyzation of the whole, all possible interpretations are both! Ultimately I would suggest that the definition of usefulness that is brought up in the comment is usefulness applied to some midpoint, one of the boxes that are unlabled. Certainly, progressing along one of the initial two division trees when the point or the idea that one is interested in is on the other is a path to confusion and uselessness. Thus only some would be useful, but still valid.
Relation of this to anything: non-zero but closer to 0, but these are the things that keep me up at night.