The Average-to-Absolute Projection Paradox (AAPP): A Cross-Domain Framework for Average-Based Projection, Distributional Information Loss, and Absolutization

Statistical averages are widely used to summarize populations, describe system-level properties, and support predictions under uncertainty. A central distinction, however, separates the use of an average as a descriptive statistic or conditional prediction from the treatment of that average as an absolute, exceptionless description of every individual realization. This manuscript proposes the Average-to-Absolute Projection Paradox (AAPP), a cross-domain conceptual framework for examining how average-based representations may be projected from an aggregate level to individual units and then absolutized beyond the evidence available. The framework preserves a height-estimation case as its primary illustration: a hypothetical population mean of 68 inches does not imply that every individual in that population has a height of 68 inches. The primary case is formalized using population means, individual deviations, variance, prediction error, loss functions, and distributional information. A proposed mechanism taxonomy distinguishes aggregate statistical extraction, central-value prioritization, default-mean anchoring, cross-level projection, distributional information suppression, projection absolutization, exception discounting, projection-reality divergence, and possible feedback effects. The framework separates a psychological research branch, termed Average-Absolutization Bias, from a systems-theoretic branch, termed the Systemic Average-Absolutization Mechanism. It proposes operational definitions, a dimensionless heterogeneity measure, a task-relative discrepancy index, testable hypotheses, boundary conditions, falsification criteria, a simulation design, and an empirical research program. The manuscript does not claim that the proposed framework constitutes a validated psychological construct, a formally contradictory mathematical paradox, or an established universal law. Its principal research question is whether the transition from a useful aggregate summary to an unjustifiably absolute individual-level claim can be identified and measured in ways that provide explanatory value beyond existing work on statistical aggregation, ecological inference, anchoring, and judgment under uncertainty.Keywords: statistical averages; individual-level inference; average-based projection; absolutization; cognitive bias; systems theory; distributional information: prediction error; ecological inference; model generalization.