Position Bias is Hidden Behind Ceiling Effects: A Permutation Diagnostic for LLM Benchmarks

Abstract:Position bias in multiple-choice LLM evaluation is widely cited as a confound in capability comparisons, but published measurements rely on single answer-order shuffles whose results confound the bias signal with content-level noise and sampling stochasticity. I introduce inspect_permute, an open-source extension to the inspect_ai evaluation framework that runs exhaustive answer-order permutations per question and reports the chi-squared / Cramer V signature of position bias with bootstrap confidence intervals. I apply the tool across four vendors (gpt-4o-mini, claude-haiku-4-5, gemini-2.5-flash, grok-3) on five MMLU subjects, 24,000 API calls under temperature-0 generation, with falsifier predictions pre-registered via a public SHA-256 hash before half the data was observed. Position bias turns out to be statistically detectable only within a roughly 60-95% base-accuracy Goldilocks zone. Below it, processing-load dominance swamps subject-specific signal; above it, ceiling effects compress the variance below the chi-squared test resolution. Detectable cells separate into two mechanism types: monotone A-to-D decrease (processing_load, in low-tier models) and non-monotone D-drop (content_ambiguity, in a narrow capability band). Standard MMLU places every frontier-tier model above the detection band, so absence of signal there should be read as not measurable, not unbiased. Together with the ceiling-effect characterisation in arXiv:2606.26185, this work brackets the detectable region of position-bias measurement and makes the field central question askable in a verifiable form. Package, data, preregistration under MIT.

25 pages, 4 figures, 2 appendices. Code, data, and preregistration verification at this https URL. Companion paper: arXiv:2606.26185

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2607.20864 [cs.LG]

(or arXiv:2607.20864v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.20864 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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