This thesis focuses on the measurement of dissimilarity in the distribution of relevant economic attributes and inequality of opportunity. Equality of opportunity has gained popularity for defining the relevant equalitarian objective for the distribution of a broad range of social and economic outcomes among social groups. I show that equality of opportunity concerns in policy evaluation always rely on dissimilarity comparisons between conditional distributions, and I provide empirically testable criteria to implement these comparisons. In the first chapter, I characterize axiomatically the dissimilarity partial order for discrete conditional distributions of groups across outcome classes. I prove that, when classes are permutable, dissimilarity is rationalized by matrix majorization and implemented by checking zonotopes inclusion, while when classes are ordered the dissimilarity criterion resorts on a finite number of Lorenz majorization comparisons among groups' proportions, performed at different cumulation stages of the overall population. In the second chapter, I discuss the relevance of the dissimilarity partial order for the study of segregation at individual level. I fully characterize a well defined family of segregation indicators and I study one of them, the Gini exposure index, by using Italian data. The final chapter presents the equalization of opportunity criterion for outcome achievements. The guiding principle is that equality of opportunities is reached if there is no consensus, for a given class of preferences, in determining the disadvantaged group out of pairwise comparisons. I use the changes in (lack of) consensus on the existence and on the extent of the disadvantage to characterize the equalization of opportunity criterion. Meaningful restrictions and possible aggregation procedure are also discussed. I motivate that this criterion is identified within the rank dependent utility model, and I provide innovative inference results for inverse stochastic dominance to test it. Two applications on French data illustrate the equalizing impact of educational policies taking place early in students life.
