Political cosmopolitanism comes in many different shapes and sizes. Despite its intellectual diversity, cosmopolitanism typically agrees on one crucial matter: any prospective global democracy is best envisioned not in terms of a hierarchical world state, but instead as a multilayered system of global governance resting on an unprecedented dispersion of decision-making authority. In discarding traditional ideas of world government, cosmopolitans typically succumb to a series of mistakes. First, they presuppose unfairly dismissive accounts of world government. Second, they misleadingly contrast their own multilayered and (allegedly) institutionally novel vision to early modern (for example, Hobbesian) ideas of sovereignty, or to Max Weber's influential definition of the modern state. They thus obscure the fact that the modern state's diverse manifestations can only be partly grasped by ideal-types drawn from either Hobbes or Weber. Consequently, they depend on straw person accounts of the modern state. Third, envisioning their proposals as building on the familiar ideal of institutional checks and balances, they misconstrue the contribution that checks and balances can make to global-level democracy. Their hostility to statist ideas about global democracy notwithstanding, their proposals sometimes mimic core attributes of traditional statehood, and they tend inadvertently to ‘bring the state back in’ to global democracy.