Robust dissimilarity comparisons with categorical outcomes

The analysis of many phenomena requires partitioning societies into groups and studying the extent at which these groups are distributed with different intensities across relevant non-ordered categorical outcomes. When the groups are similarly distributed, their members have equal chances to achieve any of the attainable outcomes. Otherwise, a form of dissimilarity between groups distributions prevails. We characterize axiomatically the dissimilarity partial order of multi-group distributions defined over categorical outcomes. The main result provides an equivalent representation of this partial order by the ranking of multi-group distributions originating from the inclusion of their zonotope representations. The zonotope inclusion criterion refines (that is, is implied by) majorization conditions that are largely adopted in mainstream approaches to multi-group segregation or univariate and multivariate inequality analysis.