Mismatch between a concept’s definitional logic and its aggregation math signals conceptual confusion.

Evidence

Here the most common problems are those illustrated by the Polity democracy measure, where the semantics of the concept at the secondary level do not match the mathematics of the quantitative measure. It is not uncommon to see the logical AND at the definitional level with the use of addition or the mean at the data–indicator level. This is a signal of confusion about the concept. This is yet another reason why drawing the basic framework figure is critical: it forces one to be explicit about everything. — Gary Goertz, Social Science Concepts and Measurement, 303

Categorization

• XREF: Connects to the measurement-validity idea that a concept’s semantics must be mirrored in how its parts are aggregated — the same logic behind semantic/measurement mismatch critiques in scaling.
• SEED: Essay angle: ‘Your composite index is lying about your theory’ — cataloguing cases where an AND definition is scored with an additive index, and what that does to inference.