Quadratic Weighting as an Aggregation-Stable Power Law: Numerical Illustration and Structural Interpretation

The quadratic probability rule plays a central role in quantum theory, yet its structural origin remains conceptually debated. In this work we investigate a simple aggregation principle that naturally selects quadratic weighting. Consider microscopic contributions that combine additively into macroscopic observables, with weights assigned through a generalized power rule . We present a scaling argument showing that within this power-law family the exponent is the only value compatible with extensive scaling when independent contributions aggregate additively in the central-limit regime. To illustrate the structural stability of this exponent, we perform numerical experiments based on block aggregation of…