[derbOac]

Vitanyi -- one of the authors cited in the linked piece -- has a paper where he and his colleagues show that even though ideal compression isn't knowable/computable, you can show that two encodings approach the ideal differentially with some computable probability (I'm being vague and handwavy because it's been awhile since I've read this literature carefully). That is, if you have two encodings A and B, you can compute some probability that A is closer to ideal than B.

It's kind of a Kolmogorov/algorithmic complexity analogue of a p-value.

I think this literature/inferential paradigm in general is far less known than it should be.