Abstract

We study how much the outputs of an aligned language model vary when the same prompt is sampled repeatedly, and which property of the task predicts that variation. For each prompt we draw 25 completions, embed them, and measure their dispersion, the mean pairwise cosine distance. The central finding is that dispersion is predicted by the consensus density of the task, defined as the degree of agreement about what a good answer looks like. Three held-out judge models score consensus from the prompt alone and never see any output. Their scores predict measured dispersion at Spearman ρ = −0.91 (n = 20). The task-type ordering of dispersion holds on two unrelated models (ρ = 0.85 and 0.84). The judge-to-dispersion relation holds within two professional domains (ρ = −0.83 across 42 pharmaceutical-market prompts and −0.62 across 40 software-engineering prompts). A preliminary human expert panel tracks the judges at ρ = 0.74. The relation also holds after conditioning. The dispersion of a conditioned prompt follows that prompt's own judge-scored consensus and can fall below or rise above the unconditioned default. The surface form of the instruction does not predict the direction. A matched base-versus-instruct comparison on open weights shows that the pretrained model already has the gradient and that alignment amplifies it, compressing the high-consensus end about 8.7-fold against 1.8-fold at the low end. Absolute magnitudes drift between sampling batches. All claims therefore rest on rank correlations and effect directions, which are stable across five batches, two embedders, and four model families. In a separate section we state, as an untested hypothesis, how this gradient may relate to reports that AI equalizes outcomes on some tasks and amplifies differences on others.