Decision Noise in Threshold Selection

Can noisier threshold selection produce a group with higher mean true value? We answer this question by varying the scale of a fixed assessment error. Holding the selection rate fixed, less noise yields a first-order stochastically dominant distribution of selected values. At a fixed threshold, however, more noise can raise the selected mean even as selection loss, which weights selection mistakes by the distance of true value from the threshold, increases. Under joint Gaussianity, we characterize when the selected mean rises or falls with noise. In treatment selection, noise alone can generate subgroup differences in participants' average gains despite identical population gain distributions.