Moral Entropy: Auditing Bias and Uncertainty in Moral Judgment
Organizations: University of Luxembourg
Abstract
Most work in computational ethics treats annotator disagreement on moral content as noise to be voted away, collapsed into majority vote or the more permissive any-annotator rule the moment a single annotator flags an item. We argue this uncertainty should instead be modeled and learned from. We introduce Moral Entropy, a Bayesian framework that keeps a full posterior over the true label and decomposes its entropy into aleatoric uncertainty (irreducible disagreement about the moral content) and epistemic uncertainty (from insufficient or noisy annotation) -- and lets any heuristic consensus rule be audited against a calibrated ground truth via entropy methods such as cross-entropy/KL, Brier score, and expected calibration error. Across three corpora and fifteen discourse domains, auditing the standard aggregation rules against this posterior reveals bias that no current pipeline reports: the any-annotator rule disagrees with the calibrated posterior on roughly 30% of items -- pooled, almost entirely false positives, though the errors invert at the foundation level (19.9%/38.9% mean FPR/FNR on MFTC) -- while the stricter majority and two-vote rules miss 63-83% of true positives.
Figures & tables
| Care | Def: Aversion to others’ suffering; underlies kindness and nurturance. |
|---|---|
| Ex: “My heart breaks seeing children separated from families at the border.” | |
| Fairness | Def: Demand for equal treatment and reciprocity; underlies justice. |
| Ex: “Everyone deserves equal access to healthcare regardless of income.” | |
| Authority | Def: Deference to rank and tradition; underlies respect and duty. |
| Ex: “ Respect your elders and follow traditional values that built this nation.” | |
| Loyalty | Def: Allegiance to the in-group over outsiders; underlies patriotism. |
| Corpus | Subcorpus | Au% | Ca% | Fa% | Lo% | Sa% | #Ann. | |
|---|---|---|---|---|---|---|---|---|
| MFRC | Everyday Morality | 10.4 | 37.4 | 25.5 | 11.7 | 13.5 | 3.00 | 5,366 |
| US Politics | 19.7 | 29.6 | 38.3 | 7.7 | 8.4 | 2.99 | 5,351 | |
| French Politics | 25.4 | 16.0 | 26.0 | 13.1 | 8.0 | 3.00 | 7,169 | |
| MFRC total | 17,886 | |||||||
| MFTC | ALM | 20.9 | 61.6 | 49.8 | 26.3 | 16.9 | 3.03 | 4,326 |
| BLM | 21.3 | 56.6 | 49.5 | 27.2 | 20.8 | 4.92 | 5,117 |
| Foundation | ROC-AUC vs. Hard |
|---|---|
| Sanctity | 0.950 |
| Authority | 0.944 |
| Loyalty | 0.934 |
| Care | 0.955 |
| Fairness | 0.949 |
| Authority | Care | Fairness | Loyalty | Sanctity | ||||||
| Corpus | Ale | Epi | Ale | Epi | Ale | Epi | Ale | Epi | Ale | Epi |
| MFRC | ||||||||||
| Everyday Morality | 0.0670 | 0.0002 | 0.0542 | 0.0002 | 0.0760 | 0.0002 | 0.0661 | 0.0002 | 0.0587 | 0.0002 |
| French politics | 0.1385 | 0.0003 | 0.0348 | 0.0001 | 0.0856 | 0.0002 | 0.1420 | 0.0003 | 0.0520 | 0.0002 |
| US Politics | 0.1126 | 0.0002 | 0.0531 | 0.0002 | 0.0902 | 0.0002 | 0.0928 | 0.0002 | 0.0588 | 0.0002 |
| MFTC | ||||||||||
Annotator Disagreement
Annotator disagreement studies why human labels differ, how to measure and model that variation, and how it should shape AI training and evaluation.
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