Purpose-Relative Equivalence Through Representation: How a Representation Built for a Purpose Makes Some Differences Not Matter

This conceptual paper introduces Purpose-Relative Equivalence Through Representation, the constraint that different source states mapped to the same output become indistinguishable to any procedure relying only on that output. Whether treating those states as interchangeable is justified depends on the purpose the representation serves. The account applies to selective mappings whose domain and rule are specified. The constraint does not follow from usability alone, and reversible encodings do not merge distinct source states in this way. The assessment standard is sufficiency for the intended operation: a representation may omit extensive detail while retaining every distinction its purpose requires. The paper relates the constraint to measurement-scale theory and examines body mass index as a documented case. Its formula gives the same value to people with different body compositions. The discussion compares the criteria used to evaluate the index with later guidance limiting its use, without determining appropriate cutoffs or adequacy for particular clinical decisions. Part of the Equivalence and Interchangeability series within On Human Modeling, the paper asks what a representation merges, which use it supports, and who decides which differences can be disregarded. Its framework can inform human–AI research on whether summaries, classifications, and scores preserve the distinctions required for their intended use.