The analysis of many social phenomena requires to compare distributions of outcomes achieved by individuals belonging to different social groups, defined for instance by their gender, ethnicity, birthplace, education, age or parental background. When the groups are similarly distributed across classes of realizations, their members have equal chances to achieve any of the attainable outcomes. Otherwise, a form of dissimilarity prevails. We frame dissimilarity comparisons of sets of groups distributions by showing the equivalence between axioms underpinning information criteria, majorization conditions, agreement between dissimilarity indicators and new empirical tests based on Zonotopes and Path Polytopes inclusion. Multi-group comparisons of segregation, discrimination and mobility, as well as inequality evaluations, are embedded within the dissimilarity model.
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