This paper aims to develop a geometry of moral systems. Existing social choice mechanisms predominantly employ simple structures, such as rankings. A mathematical metric among moral systems allows us to represent complex sets of views in a multidimensional geometry. Such a metric can serve to diagnose structural issues, test existing mechanisms of social choice or engender new mechanisms. It also may be used to replace active social choice mechanisms with information-based passive ones, shifting the operational burden.
Under reasonable assumptions, moral systems correspond to computational black boxes, which can be represented by conditional probability distributions of responses to situations. In the presence of a probability distribution over situations and a metric among responses, codifying our intuition, we can derive a sensible metric among moral systems.
Within the developed framework, the author offers a set of well-behaved candidate metrics that may be employed in real applications. The author also proposes a variety of practical applications to social choice, both diagnostic and generative.
The proffered framework, derived metrics and proposed applications to social choice represent a new paradigm and offer potential improvements and alternatives to existing social choice mechanisms. They also can serve as the staging point for research in a number of directions.
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