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.