'Beautiful' needs 2 places because our concept of beauty admits of perceptual variation. 'Fairness' does not grammatically need an 'according to whom?' argument place, because our concept of fairness is not observer-relative.

What? It seems to me that fairness and beauty are equally subjective, and the intuition that says "but my sense of fairness is objectively correct!" is the same intuition that says "but my sense of beauty is objectively correct!"

If we can logically pinpoint 'fairness,' then fairness can be rigorously and objectively discussed even if some species find the concept loathsome

I agree that we can logically pinpoint any specific concept; to use the pie example, Yancy uses the concept of "splitting windfalls equally by weight" and Zaire uses the concept of "splitting windfalls equally by desire." What I disagree with is the proposition that there is this well-defined and objective concept of "fair" that, in the given situation, points to "splitting windfalls equally by weight."

One could put forward the axiom that "splitting windfalls equally by weight is fair", just like one can put forward the axiom that "zero is not the successor of any number," but we are no closer to that axiom having any decision-making weight; it is just a model, and for it to be used it needs to be a useful and appropriate model.