Toward a Mathematical Theory of Moral Systems

In this monograph we attempt to mathematically codify a notion of "moral systems," and define a sensible measure of distances between them. Along the way we delve into a number of related topics, and propose mathematical proxies for otherwise vague concepts such as hypocrisy, judgment, world-view, and moral trajectory. In addition to detailed derivation of a number of candidate metrics, we offer several examples, including a concrete distance calculation for a simple system. The framework we develop is not confined to the analysis of moral systems, and may find use in a wide variety of applications involving decision systems, black box computation, or conditional probability distributions.