This position paper argues that researchers should not only study how human biases enter large language models (LLMs), but actively leverage those biases as diagnostic tools to surface society’s "unwritten code"—the tacit norms and hidden heuristics that govern high-stakes decisions yet resist explicit articulation. We present a case study in peer review: a framework that iteratively pushes LLMs to generate self-consistent hypotheses explaining score differences across 26,731 submissions to 46 conferences. LLMs’ normative priors (cues extracted by self-talk) emphasizing theoretical rigor are systematically updated toward posteriors (cues actually used in the judgment) emphasizing storytelling and contextualization—a finding cross-validated by independent human survey evidence. Human reviewers explicitly reward prior-aligned aspects (r=0.49) but rarely articulate the storytelling posteriors (r=-0.14), despite implicitly rewarding them. These findings generalize to out-of-sample judgment and different models. We argue this framework applies to hiring, admissions, and criminal justice, offering a scalable path to making hidden evaluative codes visible for public scrutiny and equitable reform.