We propose a model of labor market sector self-selection that combines comparative advantage, as in the Roy model, and sector composition preference. Two groups choose between two sectors based on heterogeneous potential incomes and group compositions in each sector. Potential incomes incorporate group specific human capital accumulation and wage discrimination. Composition preferences are interpreted as reflecting group specific amenity preferences as well as homophily and aversion to minority status. We show that occupational segregation is amplified by the composition preferences and we highlight a resulting tension between redistribution and diversity. The model also exhibits tipping from extreme compositions to more balanced ones. Tipping occurs when a small nudge, associated with affirmative action, pushes the system to a very different equilibrium, and when the set of equilibria changes abruptly when a parameter governing the relative importance of pecuniary and composition preferences crosses a threshold.
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