Threshold-Induced Divergence: How a Line Drawn Between Similar Cases Can Make Them Diverge

This conceptual paper introduces Threshold-Induced Divergence, the mechanism by which a decision boundary separates nearby cases into categories that receive different treatment, amplifying later differences between them. It examines how differences produced by a rule can subsequently be interpreted as characteristics that existed before the rule applied. The account distinguishes the discontinuity specified by a threshold from the subsequent divergence that requires empirical evidence. Its assessment standard asks whether explanations separate prior differences from those produced by treatment. Comparing cases near a boundary can help, provided the assumptions needed to attribute differences to the threshold are supported. The paper relates the mechanism to regression discontinuity designs and discusses research on China’s Huai River heating policy. That study estimated differences in pollution and life expectancy across a policy boundary. It supports a threshold-produced difference under its identifying assumptions; it does not trace how a gap between initially matched places grew over time. Part of the Relational Conditions and Dynamics series within On Human Modeling, the paper offers questions for examining classification boundaries, their consequences, and who can contest them. These questions can inform human–AI research on decision thresholds and the interpretation of group differences following automated classification.