The arithmetic mean gives moderate, not perfect, substitutability among components

Evidence

An important general misconception is that the mean implements “perfect substitutability.” The UNDP says, “Using the arithmetic mean allows perfect substitutability between mean years of schooling and expected years of schooling” (UNDP 2018b, 2) or “The twentieth Human Development Report introduced a new version of the HDI. The main change is that the authors relax the HDI’s past assumption of perfect substitutability between its three components” (Ravallion 2016, 85). It is not clear what perfect substitutability means in this literature. Substitutability varies along a continuum: the mean is not “perfect” in any usual sense because it is in the middle of the substitutability continuum. Because of this use of the term “perfect substitutability,” I use the term “complete substitutability.” The mean offers in fact limited substitutability for reasons discussed above. — Gary Goertz, Social Science Concepts and Measurement, 1019

Categorization

• DEFINE: Distinguishes ‘perfect substitutability’ (the misleading UNDP term) from ‘complete substitutability,’ and locates the mean mid-way on the substitutability continuum.
• XREF: Connects to multidimensional index construction (HDI, V-Dem) and to the logic of weakest-link vs best-shot aggregation in development and democracy measurement.