Robust dissimilarity comparisons with categorical outcomes

The analysis of many economic phenomena requires partitioning societies into groups, identified for instance, by gender, ethnicity, birthplace, education, age or parental background, and studying the extent at which these groups are distributed with different intensities across relevant outcomes, like jobs, locations, schools, policy treatments. When the groups are similarly distributed, their members could be seen as having equal chances to achieve any of the attainable outcomes. Otherwise, a form of dissimilarity prevails. We frame dissimilarity comparisons of multi-group distributions defined over categorical outcomes by showing the equivalence between axioms underpinning information criteria, majorization conditions, agreement between dissimilarity indicators and new empirical tests based on Zonotopes inclusion. Mainstream approaches to two- and multi-group segregation as well uni- and multivariate inequality analysis are shown to be nested within the dissimilarity model.