Operationalizing Dyadic Calibration, Miscalibration, and Positive-Sum Degradation - DSS IVa

This preprint provides the quantitative operationalisation and measurement architecture for the theoretical constructs developed in DSS-I through DSS-III. The paper defines calibration as correspondence between partners’ representations of dyadic organisation rather than equality of role shares. It therefore rejects externally imposed symmetry benchmarks and instead constructs dyad-internal reference frames from partners’ own representations of responsibilities, constraints, and domain structure. The proposed elicitation architecture includes self-allocation, partner-allocation, domain salience, and optional contextual and gating indicators. From these inputs, the paper derives measures of self-offset, dyadic dispersion, salience-weighted miscalibration, aggregate coordination cost, and attributional divergence. These metrics distinguish absolute role level from representational alignment and preserve the difference between local and global coherence. They allow an apparently balanced dyad to be identified as locally miscalibrated in a highly salient domain, while also allowing asymmetric arrangements to be represented as coherent when partners share a compatible internal map. The measures are linked to the hypotheses developed in DSS-I through DSS-III and are compatible with cross-sectional, longitudinal, APIM, EMA, and DSEM designs. The framework is methodological and diagnostic rather than normative or therapeutic. Its indices do not measure fairness, effort, individual merit, relationship quality, pathology, or preferred outcomes. Mathematics in the Dyadic Systems Series is representational rather than foundational. Formal notation is used to make proposed mechanisms, constraints, dependencies, and directional tendencies explicit, internally consistent, and empirically addressable. The equations are neither exhaustive descriptions of lived relational dynamics nor claims that dyads perform numerical optimisation. Formalisation provides a disciplined language through which the proposed measurement architecture can be communicated, examined, and tested.