# Moral Entropy: Auditing Bias and Uncertainty in Moral Judgment

arXiv: https://arxiv.org/abs/2609.21992 · HTML: https://mlsanity.com/paper/2609.21992/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 13 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 3 of 3)

- [MoralBERT: A Fine-Tuned Language Model for Capturing Moral Values in Social Discussions](https://mlsanity.com/paper/2403.07678/) (2024)
- [Beyond Human Judgment: A Bayesian Evaluation of LLMs' Moral Values Understanding](https://mlsanity.com/paper/2508.13804/) (2025)
- [Moral Semantics Survive Machine Translation: Cross-Lingual Evidence from Moral Foundations Corpora](https://mlsanity.com/paper/2605.22660/) (2026)

## Abstract (arXiv)

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.