An Algebraic Exposition of the Theory of Dyadic Morality
Kush R. Varshney
Formalizing the psychological model of dyadic morality โ agent causes harm to patient โ using structural causal modeling notation, this paper introduces three operators that extend standard SCM to capture human moral judgment: a typecasting operator (classifying agents and patients), a completion operator (inferring missing causal links), and a valence-dependent inference mechanism. It also addresses how the inherently two-node model handles complex multi-party scenarios via node collapse and sequential processing, then maps these constructs onto AI policy problems like detecting conflicting obligations and structuring helpfulness policies.
No production traction yet โ zero citations and all GitHub references are arXiv feed aggregators, not implementations. The work is purely theoretical and primarily of interest to researchers building neurosymbolic or value-aligned AI systems; anyone hoping to operationalize it will need to do substantial empirical grounding work, which the paper itself acknowledges as future work through its recommendation for scoped, contextual measurement of mind perception.
This paper provides an algebraic exposition of the theory of dyadic morality (TDM), a psychological model of moral judgment grounded in a simple two-node template: an intentional agent causing harm to a vulnerable patient. We formalize TDM using structural causal modeling (SCM) notation and identify three psychological operators (typecasting operator, completion operator, and valence-dependent inference mechanism) that extend standard SCM to capture how people compute moral judgments under constraints. We address scalability challenges arising from TDM's dyadic limitation, showing how moral cognition compresses multi-node scenarios through node collapse and sequential processing. Drawing on this algebraic framework, we demonstrate concrete applications to AI policy design: detecting conflicting obligations, structuring helpfulness policies to preserve user agency, and designing post-failure communication as causal interventions. Finally, we recommend scoped, contextual measurement of mind perception over universal averaging to operationalize the theory empirically. This algebraic formalization enables neurosymbolic AI systems to compute morality in a way that is both mathematically rigorous and faithful to human moral cognition.