Unifying approaches to consensus across different preference representations

Consensus measures can be useful in group decision making problems both to guide users toward more reasonable judgments and to give an overall indication of the support for the final decision. The level of consensus between decision makers can be measured in contexts where preferences over alternatives are expressed either as evaluations or scores, pairwise preferences, and weak orders, however these different representations often call for different approaches to consensus measurements. In this paper, we look at the distance metrics used to construct consensus measures in each of these settings and how consistent these are for preference profiles when they are converted from one representation to another. We develop some methods for consistent approaches across decision making settings and provide an example to help investigate differences between some of the commonly used distances.