Competence models are typically created and explored by a small number of experts. Boole, Gentzen, Kolmogorov, Ramsey, De Finetti, … The authority can often be shifted to the mathematics. However, although non-experts can usually understand a statement of the theorem to proved, often they can’t understand the details of the proof.
There are problems with being an expert. If you stare too long at the formalism, then you lose your intuition, and can’t see why someone would interpret a task “the wrong” way. Often there are a priori non-obvious interpretations.
And who decides what constitutes a permissible interpretation? Some obvious ideas for this are open to debate. For instance, is it always reasonable for people to keep their interpretation constant across tasks? Or is it rational to change your mind as you learn more about a problem? Is it rational to be aware of when you change your mind?
To complicate things further, various measures loading on g predict interpretations. Does that mean that those who have better cognitive ability can be thought of as having reasoned to the correct interpretation?