The Human Moral Archive Framework (HMAF): Addendum I – Formalizing the Moral Distribution Model (MDM)

This addendum extends The Human Moral Archive Framework (HMAF) by formalizing the Moral Distribution Model (MDM)—a mathematical and empirical construct for representing the moral variability, aggregation, and transferability of human ethical dispositions. While the HMAF established a foundation for capturing moral cognition as empirically observable data, the MDM introduces the notion of moral probability fields, enabling computational moral reasoning that reflects human ethical weighting across time and culture. Defining examples—from global attitudes toward euthanasia and data privacy to measurable temporal drift in views on same-sex marriage—illustrate how moral data can be modeled statistically rather than declaratively. This formalization marks a pivotal shift from descriptive moral archiving to predictive and adaptive ethical modeling, advancing the prospect of empirical machine ethics. In addition, the Moral Density Function (MDF) is introduced as the probabilistic substrate underlying the MDM, allowing for comparative measurement of moral convergence and divergence across populations and epochs. Together, these constructs extend the HMAF toward a unified framework for the quantification and analysis of moral fields within empirical moral data science. This document serves as Addendum I to “The Human Moral Archive Framework (HMAF): A Structural Foundation for Empirical Machine Ethics” (Otto, 2025). It introduces the Moral Distribution Model (MDM) and Moral Density Function (MDF) as formal extensions of HMAF.