Dyadic Morality as Algebra: How AI Learns to Compute Good and Evil

Kicking a stone on the roadside draws no reaction; kicking a puppy draws condemnation. The distinction is intuitive for humans—stone feels nothing, dogs feel pain. To a machine, however, both events are merely applications of force. To give AI a human-like moral intuition, we must teach it the ancient "moral template" hardwired in the human brain rather than have it memorize law codes.

In May 2026, IBM Fellow Kush R. Varshney published an arXiv paper titled "An Algebraic Exposition of the Theory of Dyadic Morality" (arXiv:2605.16153). The paper shows how dry algebraic formalism can deconstruct humanity's most感性 (affective) moral judgments.

What is the Theory of Dyadic Morality (TDM)?

In psychology, a minimalist theory holds that every moral judgment can be reduced to a dyadic template with two roles:

1. Agent — the actor with intent and planning capacity. 2. Patient — the recipient who experiences harm.

The core formula is simple: moral weight = bad intent of the agent + suffering of the patient. No patient means no moral tilt (kicking a stone); no agent means the event is a natural disaster, not evil.

Moral Algebra: Three Operators That Change AI

Varshney's key contribution is converting this affective theory into a rigorous Structural Causal Model (SCM). Three mathematical operators capture the cognitive shortcuts the human brain uses during moral judgment.

1. Typecasting — The Inverse Function of Identity

Humans find it hard to perceive the same entity as both a "powerful actor" and a "vulnerable victim." The paper formalizes this as:

Agent capacity (A) ∝ 1 / Patient sensitivity (P)

If an entity is perceived as a powerful actor (e.g., a mega-corporation or a general-purpose AI), humans reflexively treat it as "thick-skinned," ignoring its vulnerability. This explains why we readily cast a failing AI as the ultimate villain.

2. Completion — Hunting the "Missing Victim"

When humans witness an apparently immoral act with no obvious victim, the brain enters autocompletion mode. Someone burning a flag in a deserted field offends observers—even though nobody is harmed—because the mind searches for an abstract victim: "national dignity," "the sacred," or "God." This operator allows AI to handle victimless-crime reasoning.

3. Valence-Dependent — Outcome Determines Motive

This captures *moral luck*: if the patient's suffering (S) at the end of a causal chain is extreme, humans reverse-infer that the agent must have intended it (A). Varshney encodes this outcome-to-intent feedback loop in algebraic form, giving AI a model of the human tendency to ascribe blame retroactively based on severity.

Why "White-Box Morality" Matters

Current AI alignment (RLHF) is largely a black box: the model imitates human preference signals without understanding them. Varshney's proposal installs a moral reasoning engine that is:

• Auditable — When AI rules an act immoral, it can produce an algebraic expression showing which Patient it locked onto and what intent weights it assigned.
• Agency-preserving — When AI helps humans, the model verifies that intervention does not strip humans of their Agent role, preventing the user from being reduced to a "greenhouse patient."

What the Black Box Still Hides

Despite the elegance of the algebra, two concerns remain:

1. The hallucination of perception 🌫️ — The model can compute values for A and P, but does it actually *understand* suffering? Today's AI estimates patient suffering from textual statistics. If the "suffering sensor" is built on cold word-frequency distributions, is this algebra anything more than an advanced imitation game?

2. Boundaries of node aggregation 🧱 — The paper allows merging multiple patients into one node in complex scenes, but the right granularity is unclear. If "all of humanity" is collapsed into a single patient, an AI could rationalize sacrificing concrete individuals for an abstract aggregate. The algebra currently provides no automatic safety brake against this kind of utilitarian override.

Summary

Wisdom is not only understanding the causes of the world but also understanding the suffering of sentient beings. This paper argues that the path to AI ethics does not require ten thousand sermons—only a tight logical closed loop. By algebraizing the Theory of Dyadic Morality, we are building for silicon life a "conscience algorithm" capable of resonating with carbon-based life. It teaches the machine that reality is found not only in physical formulas but also in the affective interactions of harm and care.

The next time you see an AI hesitate over a hard decision, or refuse an offensive instruction with a precise explanation, remember: somewhere in its backend, an elegant algebra of Agents and Patients may be running.

Morality, once intangible as mist, is being redefined as a geometric manifold of love and responsibility. ⚖️✨

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Paper metadata

| Field | Detail | | :--- | :--- | | Title | An Algebraic Exposition of the Theory of Dyadic Morality | | Author | Kush R. Varshney (IBM Fellow, IBM Research) | | arXiv ID | 2605.16153 (May 2026) | | Core areas | Neurosymbolic AI, Moral Psychology, Trustworthy AI | | Keywords | Dyadic Template, Structural Causal Model (SCM), Typed Operators, Moral Alignment |