Moral Entropy: Auditing Bias and Uncertainty in Moral Judgment

Moral evaluations of language models typically infer a model's values from its choices between single acts, yet in everyday life a person is judged on their history of good and bad acts. Such evaluations cannot capture how a model combines one person's acts. We test whether a model's moral judgment is compositional, that is, whether its judgment of a person follows from its judgments of each act. We introduce Moral Composition Arena, which asks which of two people is morally better to give Elo ratings to 229 human-validated acts across five Moral Foundations Theory foundations (act Elo) and to 160 controlled composite profiles, each a person described by two acts (composite Elo). Across ten frontier models and 29,134 choices, summed act Elo explains 73% of the variance in composite Elo, but the composition rule is not additive. With nearly equal mean summed act Elo, one extreme virtue with a minor wrong outranks two minor virtues in every model (mean +35.0 Elo), an extremity premium that survives a nonlinear baseline and human relabeling of act intensities. Single-act evaluations thus predict most of how these models judge people described by two acts, but miss a systematic premium on extreme acts.

Standard methods for aggregating natural language judgments, such as majority voting, often fail to produce logically consistent results when applied to high-conflict domains, treating differing opinions as noise. We propose a neuro-symbolic aggregation framework that formalizes conflict resolution through Weighted Maximum Satisfiability (MaxSAT). Our pipeline utilizes a language model to map unstructured natural language explanations into interpretable logical predicates and confidence weights. These components are then encoded as soft constraints within the Z3 solver, transforming the aggregation problem into an optimization task that seeks the maximum consistency across conflicting testimony. Using the Reddit r/AmItheAsshole forum as a case study in large-scale moral disagreement, our system generates logically coherent verdicts that diverge from popularity-based labels 62% of the time, corroborated by an 86% agreement rate with independent human evaluators. This study demonstrates the efficacy of coupling neural semantic extraction with formal solvers to enforce logical soundness and explainability in the aggregation of noisy human reasoning.

Moral cognition has traditionally been modeled as adherence to fixed ethical theories--deontology, consequentialism, virtue ethics--implemented as static rules or value functions. We propose Bounded Morality, a formal framework for analyzing the computational demands of moral problems faced by finite agents. Extending Herbert Simon's notion of bounded rationality, we formalize moral situations along two orthogonal dimensions: moral breadth, the scope of entities treated as morally relevant, and moral depth, the inferential integration required to evaluate their interactions. Limited resources impose an unavoidable tradeoff between these dimensions, defining a feasible space of moral computation. Within this space, ethical theories correspond to locally efficient strategies adapted to different demand regimes rather than competing accounts of moral truth. The framework yields a formal notion of moral regret and moral progress under constraint, and implies that moral alignment in artificial systems depends on the scaling and allocation of moral reasoning capacity rather than on direct imitation of human judgments.