AI Detectors Fail Diverse Student Populations: A Mathematical Framing of Structural Detection Limits
This addresses the issue of unfair AI detection in educational settings for diverse student groups, highlighting a fundamental limitation that is incremental in framing but has practical implications.
The paper tackles the problem of AI text detectors producing high false positive rates, especially against certain student populations, by mathematically showing that any one-shot detector must have a false accusation rate governed by the overlap between student writing and AI output distributions, independent of detector quality.
Student experiences and empirical studies report that "black box" AI text detectors produce high false positive rates with disproportionate errors against certain student populations, yet typically theoretical analyses model detection as a test between two known distributions for human and AI prose. This framing omits the structural feature of university assessment whereby an assessor generally does not know the individual student's writing distribution, making the null hypothesis composite. Standard application of the variational characterisation of total variation distance to this composite null shows trade-off bounds that any text-only, one-shot detector with useful power must produce false accusations at a rate governed by the distributional overlap between student writing and AI output. This is a constraint arising from population diversity that is logically independent of AI model quality and cannot be overcome by better detector engineering or technology. A subgroup mixture bound connects these quantities to observable demographic groups, providing a theoretical basis for the disparate impact patterns documented empirically. We propose suggestions to improve policy and practice, and argue that detection scores should not serve as sole evidence in misconduct proceedings.