An Algebraic Exposition of the Theory of Dyadic Morality

Summary

Varshney gives an algebraic exposition of the theory of dyadic morality (TDM), a descriptive psychology model in which moral judgment is compressed into an intentional agent, a vulnerable patient, and a harmful causal edge. The paper writes TDM in structural-causal notation, then adds non-standard psychological operators for typecasting, completion, and valence-dependent inference.

The main wiki takeaway is that TDM can be treated as a compact symbolic layer for moral-cognition modeling, but it is not a standard SCM. It uses SCM-like variables for agency, vulnerability, harm, suffering, and wrongness, then adds constraints that intentionally violate ordinary causal-independence assumptions. See Dyadic Morality for the concept and Dyadic Morality Algebra for the reusable equations.

Key Claims

• Human moral judgment is modeled by a dyadic template: an intentional agent A causes harm H to a vulnerable patient P, producing perceived wrongness W.
• Differences between publics or communities are framed as differences in perceived agency, patiency, and causality rather than as differences in the core moral-computation template.
• Three operators extend the SCM-like base model: moral typecasting inversely couples perceived agency and vulnerability; completion fills missing agent or patient nodes; and valence-dependent inference lets observed suffering increase inferred intentionality.
• Multi-node moral situations are compressed rather than expanded: groups become supernodes, responsibility or vulnerability can be diluted across large populations, and indirect harms are processed as sequential dyads.
• The framework is proposed for AI policy design by shifting from lists of prohibited behavior to patient-centric reasoning about who can suffer, how agency is bounded, and how failures should be explained.
• Empirical operationalization should be scoped to communities or stakeholder groups, because globally averaged mind-perception estimates can erase culturally meaningful variation.

Methods / Formalism

• The base dyad is A -H-> P, where A is perceived intentionality, P is perceived vulnerability or experience, and H is perceived causal harm.
• The SCM-style setup uses endogenous variables A, P, H, S, and W with equations of the form A=f_A(U_A), P=f_P(U_P), H=f_H(U_H), S=f_S(P,H,U_S), and W=f_W(A,S,U_W).
• The paper later writes a compact wrongness factor as:

$$W=k(A\times P\times H{)}^{\alpha },$$

where k depends on scenario semantics and alpha is a sensitivity parameter.

• Typecasting is sketched as an inverse constraint between agency and vulnerability, completion as C(O) -> {A,P}, valence-dependent inference as A_inferred=g(valence(S), A), and evidential moral inference as Pr(A|S,H) proportional Pr(S|A,H) Pr(A).
• Scalability mechanisms include node collapse, fractional agency or vulnerability under group supernodes, and sequential dyads with W_total = W_1 + W_2.
• Scope assumptions: this is an expository mathematization of TDM rather than new empirical evidence for the psychology; it explicitly aims at neurosymbolic and policy-design uses.

Evidence / Experiments

• The paper is primarily formal and conceptual, not experimental.
• Empirical support is imported from the TDM literature, mind-perception work, the Knobe effect, and recent work on LLM moral reasoning, LLM social-identity bias, and simulated behavioral evidence.
• The AI-policy sections are design implications and examples rather than evaluated deployed systems.

Connections

• Dyadic Morality captures the descriptive model of moral judgment as agent-patient-harm compression.
• Dyadic Morality Algebra records the source’s reusable formal payload, including SCM-style variables, psychological operators, node collapse, sequential processing, and scoped measurement.
• Structural Equation Models supply the notation, but the paper’s extra edges and evidential back-filling mean TDM should not be read as a conventional causal DAG.
• Actual Causality is adjacent because the paper uses counterfactual appraisal such as asking whether outrage remains under a do(A=0) style intervention.
• Ghasemi2025 - Toward Virtuous Reinforcement Learning is a nearby machine-ethics source, while Varshney gives a more explicit symbolic model of moral judgment.
• Parker2024 - Responsibility in a Multi-Value Strategic Setting is adjacent on formal moral reasoning, but focuses on strategy-level responsibility over value bases rather than mind-perception compression.
• Safe Reinforcement Learning and Corrigibility connect through the paper’s patient-centric AI-safety and human-agency-preserving helpfulness recommendations.

Open Questions

• Can the proposed algebra be validated as a predictor of human judgments across communities without merely reproducing LLM training-set biases?
• How should patient-centric TDM reasoning be combined with hard safety guarantees such as Shielding or verified policy constraints?
• When should an AI system compute descriptive human moral judgment, and when should it deliberately depart from it for normative or rights-based reasons?
• How tractable is graph-editing conflict resolution when many obligations, stakeholders, and causal chains are active at once?

Citation

Varshney, K. R. (2026). An Algebraic Exposition of the Theory of Dyadic Morality. arXiv:2605.16153v1.