The Geometry of LLM-as-Judge: Why Inter-LLM Consensus Is Not Human Alignment

LLM judges now score most open-ended NLP output, and their mutual agreement is routinely read as evidence that the scores can be trusted. That reading is unsafe: judges may agree because they capture quality, or because they share the same blind spots, and agreement statistics alone cannot tell these apart. We develop a geometric test that can. Treating each judge's scores as a vector, we measure spread, effective rank, the angle to human scores, and the judge-judge, judge-human, and human-human agreement triple for 42 judges on two community-built Indic benchmarks covering four domains and eight languages. Every comparison is reference-matched: a judge and a held-out rater are scored against the same two-rater mean, since an averaged reference otherwise flatters judges by several degrees. On subjective rubrics, judges agree with one another as much as humans do yet reach only 58-66% of human agreement and often concentrate on an axis humans do not weight. On the one rubric with a verifiable answer, most of that gap closes. Ensembles converge on the judges' shared axis rather than the human one, and training widens scores without rotating them. Inter-judge agreement is evidence of human alignment only after this check passes.