McDonaldization as Dimensional Interlock: A Modeling Synthesis of Rationalization, Proxy Gaps, and Conditional Capability Lock

This paper models Ritzer's four dimensions of McDonaldization (efficiency, calculability, predictability, control) and asks when they become mutual complements. The primitive is a multiplicative gap-degradation payoff: a scalar calculability proxy opens a monetized Goodhart gap between measured success and true welfare, and the other three dimensions set the amount of unmeasured quality that standardization destroys. The mathematics is elementary and the contribution is a modeling result with a sharp falsifiable boundary, not new technique. The central result is a characterization rather than an existence claim. Differentiating the payoff yields six nonnegative own-coordinate cross-partials, and strict complementarity between any pair of dimensions holds if and only if both the relevant Goodhart-gap factor and the relevant degradation channel are nonzero. The "if and only if" is exact because every factor is nonnegative. The empirical boundary follows immediately: a faithful metric predicts no interlock at all, while an unfaithful scalar metric plus positive standardization interactions predicts that efficiency, predictability, and control become jointly more complementary once the metric becomes central. This separates the mechanism from a single-axis efficiency account, which predicts cost-cutting but not the full positive cross-partial matrix. Standard supermodular-game theory (Topkis, Vives, Zhou, Milgrom-Shannon) then gives a complete lattice of equilibria whose extremal points rise monotonically in proxy-gap salience and mimetic pressure. The iron-cage conclusion is explicitly conditional: rationalization drives the induced state monotonically toward a foreclosure region imported from a companion substrate theory, but reaches a radical-monopoly lock only under an additional margin-crossing condition plus imported returnability and preferability hypotheses. Without the crossing, the result is dimensional interlock, not lock-in. Supporting mechanisms (the lock, commons under-provision, minimum-subsidy impossibility, on-path non-identification, regulatory non-monotonicity, and mimetic spectral amplification) are imported as labeled black-box lemmas from three companion papers and are not reproved. Four further results round out the synthesis: a generator theorem showing the Goodhart gap is the sole source of the interlock, so it vanishes at the faithful boundary; a Cauchy-Schwarz argument identifying the profit-maximizing proxy-blind degradation direction and a welfare-loss lower bound equal to the gap times the degradation amount; a two-level predictability result separating within-offering variance reduction from mimetic cross-population convergence; and a price-of-anarchy lower bound combining the Goodhart wedge with an imported commons wedge. The primary falsifiable prediction needs no direct measurement of the gap: after a scalar metric becomes central, the marginal returns to efficiency, predictability, and control should rise jointly, yielding the full positive cross-partial pattern. The paper keeps the sociological reading modest, offering a transparent mechanism with a benign faithful-proxy boundary and an explicit conditional route to the iron cage rather than a historical universal.