We develop a theory of institutional transition from dictatorship to minority dominant-based regimes in natural resource-dependent economies. We depart from the standard political transition framework à la Acemoglu-Robinson in four essential ways: (i) population is heterogeneous, there is a minority/majority split, heterogeneity being generic, simply reflecting subgroup size; (ii) there is no median voter in the post-dictatorship period, political and economic competition is favorable to the minority (fiscal particularism); (iii) (windfall) natural resources are introduced, and (iv) we distinguish between labor income and resources, and labor supply is endogenous. We first document empirically fiscal particularism, its connection with natural resource endowment, and the impact of both on revolutionary bursts. Second, we construct a full-fledged model incorporating the four characteristics outlined above. We show, among others, that polarization is a sufficient condition for revolutions, while natural resource rents are not although they do matter when polarization is low. In agreement with our empirical facts, countries engaging in revolutions tend to be slightly less natural resource-rich than other countries. We also outline the interplay between natural resource rents, polarization and labor market conditions at the dawn of institutional change. Our theory is appropriate to understand the institutional dynamics of highly homogeneous natural resource-rich countries which, after a post-independence autocratic regime, turn to be dominated by minorities.