Quality resists a single ordering.

Semantic precision, evidential sufficiency, instructional usefulness, and measurement validity are not interchangeable units. Their coexistence does not imply that they can be collapsed into a universal ranking without loss.

An aggregate can conceal the very defect that a particular evaluation dimension is intended to expose. A strong result on one axis may compensate numerically for a failure that should not be compensable at all. The choice of aggregation is therefore a substantive commitment about admissible trade-offs, not a neutral presentation decision.

The distinction becomes sharper when the observables are conditional on different populations, evaluators, or task distributions. Comparing their magnitudes presupposes a common reference frame. Where that frame is absent, numerical precision can exceed interpretive precision.

A more precise number does not necessarily license a more precise conclusion.

Partial orderings, reference dependence, and estimand drift +

A partial ordering can preserve incomparability where a total ordering must manufacture a preference. Scalarization resolves that incomparability by imposing exchange rates among objectives, whether or not those rates are explicit. A resulting optimum is conditional on the imposed preference structure.

Reference dependence adds a second layer. Changes in the sampling frame, evaluator, admissible response set, or treatment of unresolved cases can change the estimand while leaving the metric’s name unchanged. Nominally comparable results may then answer different questions.

For an assessment claim, the burden is not merely to report a value, but to preserve the identity of the quantity being interpreted across the contexts in which the claim is made.