Studies investigating invariance have often been limited to measurement or prediction invariance. Selection invariance, wherein the use of test scores for classification results in equivalent classification accuracy between groups, has received comparatively little attention in the psychometric literature. Previous research suggests that some form of selection bias (lack of selection invariance) will exist in most testing contexts, where classification decisions are made, even when meeting the conditions of measurement invariance. We define this conflict between measurement and selection invariance as the invariance paradox. Previous research has found test reliability to be an important factor in minimizing selection bias. This study demonstrates that the location of maximum test information may be a more important factor than overall test reliability in minimizing decision errors between groups.